Дисертації: "Defect Conformal Field Theories"

1

Meineri, Marco. "Defects in Conformal Field Theories." Doctoral thesis, Scuola Normale Superiore, 2016. http://hdl.handle.net/11384/85893.

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2

Linke, Yannick [Verfasser], and Volker [Akademischer Betreuer] Schomerus. "Defects in Conformal Field Theories / Yannick Linke ; Betreuer: Volker Schomerus." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/117142728X/34.

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3

Jaud, Daniel [Verfasser], and Ilka [Akademischer Betreuer] Brunner. "Topological defects in conformal field theories, entanglement entropy and indices / Daniel Jaud ; Betreuer: Ilka Brunner." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2017. http://d-nb.info/1139977989/34.

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4

Quella, Thomas. "Asymmetrically gauged coset theories and symmetry breaking D-branes." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2003. http://dx.doi.org/10.18452/14909.

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Анотація:

Auf sehr kleinen Längenskalen erlaubt die Weltflächenbeschreibung über zweidimensionale konforme Feldtheorien eine störungstheoretische Definition der String-Theorie. Viele strukturelle Eigenschaften und phänomenologische Implikationen der letzteren können mit Hilfe von D(irichlet)-Branen untersucht werden, die in der zugrunde liegenden Weltflächentheorie durch konforme Randbedingungen beschrieben werden. Etliche interessante Hintergründe für die String-Theorie erhält man über Gruppenmannigfaltigkeiten und Coset-Modelle. Neben wichtigen Beispielen wie SL(2,R), SU(2) und Gepner-Modellen, die für AdS- und Calabi-Yau-Kompaktifizierungen eine Rolle spielen, beinhalten sie außerdem weitere Beispiele wie den Nappi-Witten-Hintergrund oder den Raum T^11, die über eine asymmetrische Wirkung der Eichgruppe definiert sind und eine kosmologische Raumzeit mit Urknall- und Weltsturz-Singularitäten bzw. die Basis des Conifolds beschreiben. Die vorliegende Arbeit bietet eine umfassende, auf den exakten Methoden der konformen Feldtheorie beruhende Analyse von asymmetrischen Coset-Modellen. Wegen der heterotischen Natur der zugrundeliegenden Symmetriealgebra erlauben diese Modelle nur Randbedingungen, die einen Teil der Symmetrie brechen. Nach einer allgemeinen Erläuterung der Grundidee für die Konstruktion von symmetriebrechenden Randbedingungen richtet sich das Hauptaugenmerk auf WZNW- und asymmetrische Coset-Modelle, die das Fundament nahezu aller bekannten konformen Feldtheorien bilden. Mit Hilfe der erzielten Ergebnisse werden die Struktur sowie die Geometrie von D-Branen in den Gruppen SL(2,R) und SU(2), im Hintergrund AdS_3 x S^3, in der kosmologischen Nappi-Witten-Raumzeit und in T^pq-Räumen untersucht. Die Techniken, die in dieser Arbeit entwickelt werden, erlauben jedoch ebenso die Behandlung von Rändern und Kontaktstellen in (1+1)- oder 2-dimensionalen kritischen Systemen, die in der Festkörpertheorie oder der statistischen Physik auftreten. Insbesondere können Defektlinien beschrieben werden, die weder totale Reflexion noch völlige Transmission aufweisen.
At very small length scales, the world sheet approach in terms of two-dimensional conformal field theories provides a perturbative definition of string theory. Many structural properties and phenomenological implications of the latter can be explored using D(irichlet)-branes which may be identified with conformal boundary conditions in the underlying world sheet theory. Several interesting backgrounds in string theory arise from group manifolds and coset theories. Apart from prominent examples such as SL(2,R), SU(2) and Gepner models which play a role in AdS and Calabi-Yau compactifications, they also include further instances like the Nappi-Witten background or the space T^11 which are constructed using an asymmetric action of the gauge group and which describe a cosmological space-time with big-bang and big-crunch singularities and the base of the conifold, respectively. The present thesis provides a comprehensive analysis of asymmetric cosets based on the exact methods of boundary conformal field theory. Due to the heterotic nature of the underlying symmetry algebra, the models only allow for conformal boundary conditions which break parts of the bulk symmetry. The universal ideas for the construction of symmetry breaking boundary conditions are indicated and applied in detail to WZNW and asymmetric coset theories which provide the basic building blocks of almost all known conformal field theories. The general results are used to investigate the structure and shape of D-branes in the group manifolds SL(2,R) and SU(2), the background AdS_3 x S^3, the cosmological Nappi-Witten space-time and T^pq-spaces. The techniques developed in this thesis also allow for a treatment of boundaries and junctions in (1+1)- or 2-dimensional critical systems in condensed matter theory and statistical physics. In particular, they enable us to describe defect lines which go beyond full reflection or transmission.

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5

Joshi, Keith G. "Coset conformal field theories." Thesis, University of Liverpool, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359233.

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6

Montague, Paul Stewart. "Codes, lattices and conformal field theories." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386917.

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7

Bayraktaroglu, Baran. "Light-states in Conformal Field Theories." Thesis, Uppsala universitet, Teoretisk fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-442580.

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8

Bougourzi, A. Hamid. "Free field realization of extended conformal field theories." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=70279.

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I investigate the free field realization (FFR) of various extended conformal field theories (ECFT's). More specifically, I first present a systematic method that allows the construction of the exponential type screening currents in terms of free fields in the case of the ECFT's with Kac-Moody algebras. This method is explicitly illustrated through the $su(n) sb{k}$ and $sp(4) sb{k}$ Kac-Moody algebras. Then, I use the FFR to unravel the embedding structure of the Verma modules of the ECFT with a $W sb3$ algebra. This embedding structure is expressed through a set of intertwining diagrams, which in turn, is used to compute the irreducible characters of the $W sb3$ algebra. Next, I construct two FFR's for the ECFT with the $su(n) sb{k}$ parafermion algebra. Finally, I sketch the FFR of the coset model $su(n) sb{k} times su(n) sb ell/su(n) sb{k+ ell},$ which is given in terms of the fields realizing the $su(n) sb{k}$ parafermion model and an extra free field with a background charge.

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9

Bhaseen, Miraculous Joseph. "Logarithmic conformal field theories of disordered Dirac fermions." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393358.

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10

Simmons-Duffin, David. "Carving Out the Space of Conformal Field Theories." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10448.

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We study the constraints of conformal symmetry and unitarity in Conformal Field Theories (CFTs). Crossing symmetry of four-point functions implies universal bounds on operator dimensions and three-point function coefficients. These bounds can be extracted by solving a class of infinite-dimensional convex optimization problems, giving quantitative, nonperturbative results about potentially strongly coupled theories. Our results include general bounds on operator dimensions in 4d CFTs with concrete phenomenological implications, and novel determinations of critical exponents in the 3d Ising Model. We also introduce new techniques for computing conformal blocks of higher spin operators, paving the way for further studies.
Physics

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11

Ashworth, Richard Michael. "Quantum field theories having conformal and chiral symmetry." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292952.

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12

Krishnan, Ranganathan. "Spaces of conformal theories and string field theory." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28061.

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13

Couvreur, Romain. "Geometric lattice models and irrational conformal field theories." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS062.

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Dans cette thèse nous étudions différents aspects des modèles critiques non-unitaires de physique statistique en deux dimensions. Notre approche, partant de modèles discrets sur le réseau, permet d'en apprendre plus sur les théories conformes associées. Celles-ci sont non-unitaires et souvent irrationnelles, logarithmiques ou encore non-compactes. Pour commencer, le problème de l'entropie d'intrication dans des chaînes de spin non-unitaires et son interprétation dans les modèles de boucles sont considérés. Le rôle de la charge centrale effective, une quantité pertinente pour étudier aussi d'autres problèmes de ce manuscrit, y est discuté. Ensuite, nous regardons deux problèmes liés au modèle de Chalker-Coddington, une chaîne de spin supersymétrique de dimension infinie, importante pour l'étude de la transition entre plateaux dans l'effet Hall quantique entier. Puisque ce modèle a un nombre infini de degrés de liberté, il a été proposé de considérer une série de troncations. Nous présentons de nouveaux résultats basés sur cette approche et développons cette méthode dans le cadre du mouvement Brownien dans sa formulation supersymétrique. Ensuite, un nouveau modèle est proposé pour interpoler la classe A et la classe C de l'effet Hall quantique. Le modèle de Chalker-Coddington est une réalisation particulière de la classe A tandis que la classe C, qui décrit la physique de l'effet Hall quantique de spin, est relié à un modèle de percolation. Ce modèle donne un exemple de flot sous l'action du groupe de renormalisation entre une théorie conforme compacte et non-compacte. La dernière partie de cette thèse discute la classification des observables sur réseau avec une symétrie discrète. Le processus est illustré sur le modèle de Potts avec sa symétrie sous l'action du groupe des permutations et des résultats déjà connus sont étendus au cas des opérateurs non-scalaires. Cette approche est importante dans l'étude de l'indécomposabilité des modèles non-unitaires et peut être utilisée pour étudier la percolation en dimension supérieure
In this thesis we study several aspects of two-dimensional lattice models of statistical physics with non-unitary features. This bottom-up approach, starting from discrete lattice models, is helpful to understand the features of the associated conformal field theories. They are non-unitary and often irrational, logarithmic or even non-compact. First, we study the problem of the entanglement entropy in non-unitary spin chains and its interpretation in loop models. We discuss the role of the effective central charge, a relevant quantity to study the next problems in this thesis. We then address two problems related to the Chalker-Coddington model, an infinite-dimensional supersymmetric chain important for the study of the plateau transition in the integer quantum Hall effect. Since the model has an infinite number of degrees of freedom, it has been proposed to study it with a series of truncations. We present new results based on this approach and extend this methodology to the case of Brownian motion in its supersymmetric formulation. Next, a new model is proposed to interpolate between class A and class C. The Chalker-Coddington model is a particular realisation of class A whereas class C, describing the physics of the spin quantum Hall effect, can be related to a model of percolation. This interpolating model provides an example of a RG-flow between a non-compact CFT and compact one. The last part of this thesis deals with the problem of classifying observables in lattice models with discrete symmetries. The process is illustrated on the Potts model and its symmetry under the group of permutations and previous results are extended for non-scalar operators. This approach is important to study indecomposability of non-unitary models and can be used to study models such as percolation in higher dimensions

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14

Braga, Barreiros Dos Reis Nuno. "Conformal field theories with boundaries : a geometrical interpretation." Lyon, École normale supérieure (sciences), 2003. http://www.theses.fr/2003ENSL0269.

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15

Vernier, Eric. "Non compact conformal field theories in statistical mechanics." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0005/document.

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Les comportements critiques des systèmes de mécanique statistique en 2 dimensions ou de mécanique quantique en 1+1 dimensions, ainsi que certains aspects des systèmes sans interactions en 2+1 dimensions, sont efficacement décrits par les méthodes de la théorie des champs conforme et de l'intégrabilité, dont le développement a été spectaculaire au cours des 40 dernières années. Plusieurs problèmes résistent cependant toujours à une compréhension exacte, parmi lesquels celui de la transition entre plateaux dans l'Effet Hall Quantique Entier. La raison principale en est que de tels problèmes sont généralement associés à des théories non unitaires, ou théories conformes logarithmiques, dont la classification se révèle être d'une grande difficulté mathématique. Se tournant vers la recherche de modèles discrets (chaînes de spins, modèles sur réseau), dans l'espoir en particulier d'en trouver des représentations en termes de modèles exactement solubles (intégrables), on se heurte à la deuxième difficulté représentée par le fait que les théories associées sont la plupart du temps non compactes, ou en d'autres termes qu'elles donnent lieu à un continuum d'exposants critiques. En effet, le lien entre modèles discrets et théories des champs non compactes est à ce jour loin d'être compris, en particulier il a longtemps été cru que de telles théories ne pouvaient pas émerger comme limites continues de modèles discrets construits à partir d'un ensemble compact de degrés de libertés, par ailleurs les seuls qui donnent a accès à une construction systématique de solutions exactes.Dans cette thèse, on montre que le monde des modèles discrets compacts ayant une limite continue non compacte est en fait beaucoup plus grand que ce que les quelques exemples connus jusqu'ici auraient pu laisser suspecter. Plus précisément, on y présente une solution exacte par ansatz de Bethe d'une famille infinie de modèles(les modèles $a_n^{(2)}$, ainsi que quelques résultats sur les modèles $b_n^{(1)}$, où il est observé que tous ces modèles sont décrits dans un certain régime par des théories conformes non compactes. Parmi ces modèles, certains jouent un rôle important dans la description de phénomènes physiques, parmi lesquels la description de polymères en deux dimensions avec des interactions attractives et des modèles de boucles impliqués dans l'étude de modèles de Potts couplés ou dans une tentative de description de la transition entre plateaux dans l'Effet Hall par un modèle géométrique compact.On montre que l'existence insoupçonnéede limite continues non compacts pour de tels modèles peut avoir d'importantes conséquences pratiques, par exemple dans l'estimation numérique d'exposants critiques ou dans le résultats de simulations de Monte Carlo. Nos résultats sont appliqués à une meilleure compréhension de la transition theta décrivant l'effondrement des polymères en deux dimensions, et des perspectives pour une potentielle compréhension de la transition entre plateaux en termes de modèles sur réseaux sont présentées
The critical points of statistical mechanical systems in 2 dimensions or quantum mechanical systems in 1+1 dimensions (this also includes non interacting systems in 2+1 dimensions) are effciently tackled by the exact methods of conformal fieldtheory (CFT) and integrability, which have witnessed a spectacular progress during the past 40 years. Several problems have however escaped an exact understanding so far, among which the plateau transition in the Integer Quantum Hall Effect,the main reason for this being that such problems are usually associated with non unitary, logarithmic conformal field theories, the tentative classification of which leading to formidable mathematical dificulties. Turning to a lattice approach, andin particular to the quest for integrable, exactly sovable representatives of these problems, one hits the second dificulty that the associated CFTs are usually of the non compact type, or in other terms that they involve a continuum of criticalexponents. The connection between non compact field theories and lattice models or spin chains is indeed not very clear, and in particular it has long been believed that the former could not arise as the continuum limit of discrete models built out of acompact set of degrees of freedom, which are the only ones allowing for a systematic construction of exact solutions.In this thesis, we show that the world of compact lattice models/spin chains with a non compact continuum limit is much bigger than what could be expected from the few particular examples known up to this date. More precisely we propose an exact Bethe ansatz solution of an infinite family of models (the so-called $a_n^{(2)}$ models, as well as some results on the $b_n^{(1)}$ models), and show that all of these models allow for a regime described by a non compact CFT. Such models include cases ofgreat physical relevance, among which a model for two-dimensional polymers with attractive interactions and loop models involved in the description of coupled Potts models or in a tentative description of the quantum Hall plateau transition by somecompact geometrical truncation. We show that the existence of an unsuspected non compact continuum limit for such models can have dramatic practical effects, for instance on the output of numerical determination of the critical exponents or ofMonte-Carlo simulations. We put our results to use for a better understanding of the controversial theta transition describing the collapse of polymers in two dimensions, and draw perspectives on a possible understanding of the quantum Hall plateautransition by the lattice approach

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16

Migliaccio, Santiago. "Conformal bootstrap in two-dimensional conformal field theories with with non-diagonal spectrums." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS362.

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La symétrie conforme impose de très fortes contraintes sur les théories quantiques des champs. En deux dimensions, l’algèbre des symétries conformes est infinie, et les théories conformes bidimensionnelles peuvent être complètement résolubles, dans le sens où toutes leurs fonctions de corrélation peuvent être calculées. Ces théories ont un grand domaine d'application, de la théorie des cordes jusqu'aux systèmes critiques en physique statistique, et elles ont été largement étudiées pendant les dernières décennies.Dans cette thèse nous étudions les théories conformes bidimensionnelles dont l’algèbre de symétrie est celle de Virasoro, en suivant l'approche connue sous le nom de bootstrap conforme. Sous l'hypothèse de l'existence de champs dégénérés, nous généralisons le bootstrap conforme analytique aux théories avec des spectres non-diagonaux. Nous écrivons les équations qui déterminent les constantes de structure, et nous trouvons des solutions explicites en termes de fonctions spéciales. Nous validons ces résultats en faisant des calculs numériques des fonctions de corrélation à quatre points dans des modèles minimaux diagonaux et non-diagonaux, et en vérifiant que la symétrie de croisement est respectée.En outre, nous construisons une proposition pour une famille de théories conformes non-diagonales et non-rationnelles pour toute charge centrale telle que Re(c) < 13. Cette proposition est motivée par les limites des spectres des modèles minimaux de la série D. Nous réalisons des calculs numériques des fonctions à quatre points dans ces théories, et nous trouvons qu'elles obéissent à la symétrie de croisement. Ces théories peuvent être interprétées comme des extensions non-diagonales de la théorie de Liouville
Conformal symmetry imposes very strong constraints on quantum field theories. In two dimensions, the conformal symmetry algebra is infinite-dimensional, and two-dimensional conformal field theories can be completely solvable, in the sense that all their correlation functions may be computed. These theories have an ample range of applications, from string theory to critical phenomena in statistical physics, and they have been widely studied during the last decades.In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic conformal bootstrap method to theories with non-diagonal spectrums. We write the equations that determine structure constants, and find explicit solutions in terms of special functions. We validate this results by numerically computing four-point functions in diagonal and non-diagonal minimal models, and verifying that crossing symmetry is satisfied.In addition, we build a proposal for a family of non-diagonal, non-rational conformal field theories for any central charges such that Re(c) < 13. This proposal is motivated by taking limits of the spectrum of D-series minimal models. We perform numerical computations of four-point functions in these theories, and find that they satisfy crossing symmetry. These theories may be understood as non-diagonal extensions of Liouville theory

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17

Grosse, Harald, Karl-Georg Schlesinger, and grosse@doppler thp univie ac at. "Deformations of Conformal Field Theories to Models with Noncommutative." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi931.ps.

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18

Roper, W. B. "Boundary states in conformal field theories of the annulus." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.670069.

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19

Nardoni, Emily M. "Aspects of Supersymmetric Conformal Field Theories in Various Dimensions." Thesis, University of California, San Diego, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10932229.

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In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's A,D,E singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional N = 1 variants of supersymmetric QCD, with U( N_c) or SU(N_c) gauge group, N_f fundamental flavors, and adjoint matter fields X and Y appearing in W_A,D,E(X,Y) superpotentials. We explore these issues by considering various deformations of the W_A,D,E superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional N = 1 supersymmetric SU(2) gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the N = 2 Argyres-Douglas theory H₀, and a further deformation to an N = 1 SCFT with low a central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d N = 1 quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus g and n punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees p and q. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve N = 2 supersymmetry, and derive terms that account for the local data at the punctures.

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20

Huyal, Ulas. "Conformal Symmetry In Field Theory." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613136/index.pdf.

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In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.

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21

Gasbarro, Andrew David. "Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories." Thesis, Yale University, 2019. http://pqdtopen.proquest.com/#viewpdf?dispub=13851872.

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In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal window of four dimensional gauge theories with Dirac fermions and its potential applicability to beyond the standard model physics.

In the first chapter, we review some of the history of models of composite Higgs scenarios in order to motivate the study of gauge theories near the conformal window. In the second chapter we review lattice studies of a specific theory, SU(3) gauge theory with eight flavors of Dirac fermions in the fundamental representation of the gauge group. We place a particular emphasis on the light flavor-singlet scalar state appearing in the spectrum of this model and its possible role as a composite Higgs boson. We advocate an approach to characterizing nearly conformal gauge theories in which lattice calculations are used to identify the best low energy effective field theory (EFT) description of such nearly conformal gauge theories, and the lattice and EFT are then used as complementary tools to classify the generic features of the low energy physics in these theories. We present new results for maximal isospin ππ → ππ scattering on the lattice computed using Lüscher's finite volume method. This scattering study is intended to provide further data for constraining the possible EFT descriptions of nearly conformal gauge theory. In Chapter 3, we review the historical development of chiral effective theory from current algebra methods up through the chiral Lagrangian and modern effective field theory techniques. We present a new EFT framework based on the linear sigma model for describing the low lying states of nearly conformal gauge theories. We place a particular emphasis on the chiral breaking potential and the power counting of the spurion field.

In Chapter 4, we report on a new formulation of lattice quantum field theory suited for studying conformal field theories (CFTs) nonperturbatively in radial quantization. We demonstrate that this method is not only applicable to CFTs, but more generally to formulating a lattice regularization for quantum field theory on an arbitrary smooth Riemann manifold. The general procedure, which we refer to as quantum finite elements (QFE), is reviewed for scalar fields. Chapter 5 details explicit examples of numerical studies of lattice quantum field theories on curved Riemann manifolds using the QFE method. We discuss the spectral properties of the finite element Laplacian on the 2-sphere. Then we present a study of interacting scalar field theory on the 2-sphere and show that at criticality it is in close agreement with the exact c = 1/2 minimal Ising CFT to high precision. We also investigate interacting scalar field theory on [special characters omitted] x [special characters omitted]², and we report significant progress towards studying the 3D Ising conformal fixed point in radial quantization with the QFE method. In the near future, we hope for the QFE method to be used to characterize the four dimensional conformal fixed points considered in the first half of this dissertation.

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22

Cornalba, Lorenzo T. (Lorenzo Tarcisio). "Connections over spaces of conformal field theories : testing for integrablity." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28103.

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23

Lee, Jaehoon Ph D. Massachusetts Institute of Technology. "Studies of superconformal field theories using GLSM and conformal bootstrap." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99308.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 273-288).
In this thesis, we study strongly interacting superconformal field theories in two and three dimensions. In two dimensions, we investigate N = (0, 2) gauge theories using the gauged linear sigma models (GLSM). In those theories, we identify simple mechanism by which worldsheet description of H-flux satisfying Green-Schwarz Bianchi identity arises. Under the renormalization group flow, we argue that these models flow into superconformal fixed points describing string theory compactifications backgrounds with non-trivial H-flux turned on. By analyzing quantum-consistency of effective theories with such mechanism, we identify conditions under which these theories to become interacting superconformal field theories in the infrared. In three dimensions, we study maximally supersymmetric (N = 8) conformal field theories by conformal bootstrap approach. We focus on studying the four-point function of stress-tensor multiplet. The superconformal blocks for the four-point function are computed by analyzing superconformal Ward identity. Using these blocks, we study crossing symmetry constraints both numerically and analytically. Doing so, we obtain universal bounds and exact relations of N = 8 superconformal field theory data.
by Jaehoon Lee.
Ph. D.

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at, Andreas Cap@esi ac. "Boundary WZW, G/H, G/G and CS Theories." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1061.ps.

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25

Neves, Rui Gomes Mendona. "Conformal field theories on random surfaces and the non-critical string." Thesis, Durham University, 1997. http://etheses.dur.ac.uk/4750/.

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Recently, it has become increasingly clear that boundaries play a significant role in the understanding of the non-perturbative phase of the dynamics of strings. In this thesis we propose to study the effects of boundaries in non-critical string theory. We thus analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly cancellation for Polyakov's non-critical open bosonic string with Neumann, Dirichlet and free boundary conditions. Dirichlet boundary conditions on the Liouville field imply that the metric is discontinuous as the boundary is approached. We consider the semi-classical limit and argue how it singles out the free boundary conditions for the Liouville held. We define the open string susceptibility, the anomalous gravitational scaling dimensions and a new Yang-Mills Feynman mass critical exponent. Finally, we consider an application to the theory of non-critical dual membranes. We show that the strength of the leading stringy non-perturbative effects is of the order e(^-o(1/βst)), a result that mimics those found in critical string theory and in matrix models. We show how this restricts the space of consistent theories. We also identify non-critical one dimensional D-instantons as dynamical objects which exchange closed string states and calculate the order of their size. The extension to the minimal c ≤ 1 boundary conformal models is also briefly discussed.

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26

Pickering, Austin Gerard Michael. "The effective potential and conformal invariance in supersymmetric quantum field theories." Thesis, King's College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266503.

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27

Erdmenger, Johanna Karen. "Implications of conformal invariance for quantum field theories in general dimensions." Thesis, University of Cambridge, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627571.

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28

Stigner, Carl. "Hopf and Frobenius algebras in conformal field theory." Doctoral thesis, Karlstads universitet, Avdelningen för fysik och elektroteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-14456.

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There are several reasons to be interested in conformal field theories in two dimensions. Apart from arising in various physical applications, ranging from statistical mechanics to string theory, conformal field theory is a class of quantum field theories that is interesting on its own. First of all there is a large amount of symmetries. In addition, many of the interesting theories satisfy a finiteness condition, that together with the symmetries allows for a fully non-perturbative treatment, and even for a complete solution in a mathematically rigorous manner. One of the crucial tools which make such a treatment possible is provided by category theory. This thesis contains results relevant for two different classes of conformal field theory. We partly treat rational conformal field theory, but also derive results that aim at a better understanding of logarithmic conformal field theory. For rational conformal field theory, we generalize the proof that the construction of correlators, via three-dimensional topological field theory, satisfies the consistency conditions to oriented world sheets with defect lines. We also derive a classifying algebra for defects. This is a semisimple commutative associative algebra over the complex numbers whose one-dimensional representations are in bijection with the topological defect lines of the theory. Then we relax the semisimplicity condition of rational conformal field theory and consider a larger class of categories, containing non-semisimple ones, that is relevant for logarithmic conformal field theory. We obtain, for any finite-dimensional factorizable ribbon Hopf algebra H, a family of symmetric commutative Frobenius algebras in the category of bimodules over H. For any such Frobenius algebra, which can be constructed as a coend, we associate to any Riemann surface a morphism in the bimodule category. We prove that this morphism is invariant under a projective action of the mapping class group ofthe Riemann surface. This suggests to regard these morphisms as candidates for correlators of bulk fields of a full conformal field theories whose chiral data are described by the category of left-modules over H.

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29

Lotito, Matteo. "Geometric classification of 4d rank-1 N=2 superconformal field theories." University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1530880263562131.

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30

Ishimoto, Yukitaka. "Two-point functions and boundary states in boundary logarithmic conformal field theories." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.398127.

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31

Belliard, Raphaël. "Geometry of integrable systems : from topological Lax systems to conformal field theories." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066175/document.

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Cette thèse de doctorat traite d’un cadre en géométrie complexe et de méthodes pouvant y être développées pour résoudre des ensembles d’équations différentielles compatibles venant de systèmes intégrables, classiques ou quantiques, dans le contexte de la géométrie d’espaces de modules de connexions au-dessus de courbes complexes, ou surfaces de Riemann. Elle vient de l’idée en physique mathématique que les symétries des systèmes intégrables imposent aux objets d’intérêt (fonctions de partitions ou de corrélations) des contraintes algébro-différentielles nommées équations de boucles. Le but est par la suite de résoudre ces contraintes par récurrence dans des régimes dits topologiques en utilisant une procédure nommée récurrence topologique. Leurs solutions sont en général les fonctions génératrices de quantités issues de problèmes de géométrie énumérative. Étant principalement déterminées par les conditions initiales de la récurrence, on produit au passage une classification algébro-géométrique de la famille de systèmes intégrables considérée
This PhD thesis is about a framework in complex geometry and methods thereof for solving sets of compatible differential equations arising from integrable systems, classical or quantum, in the context of the geometry of moduli spaces of connections over complex curves, or Riemann surfaces. It is based on the idea in mathematical Physics that integrable systems posess symmetries that impose algebro-differential constraints, so-called loop equations, on the objects of interest (e.g. partition or correlation functions). In turn, we intend to solve these constraints recursively in certain topological regimes using a particular procedure called the topological recursion. Their solutions are in general generating functions of enumerative-geometric quantities. Since they are for the most part determined by the initial data of the recursive process, it realizes in the making an algebro-geometric classification of the family of integrable models under consideration

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32

GIORGETTI, LUCA. "Braided Actions of DHR Categories and Reconstruction of Chiral Conformal Field Theories." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2016. http://hdl.handle.net/2108/249219.

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Quantum Field Theory (QFT) is our modern understanding of particles and matter at small scales, where quantum behaviour replaces macroscopical phenomena, which are much closer to intuition, and dynamics is rather driven by the more fundamental interactions between fields. Using quantum fields one can describe particle production, annihilation and scattering processes and they can all together be cast into the Standard Model of particle physics. The latter gives a recipe to predict cross sections of high-energy collisions which fit remarkably well with experimental data. On the other hand our mathematical understanding of the framework, and how to replace diverging series, ad hoc renormalized or truncated to get finite numbers, is still a deep open question. Since the early days it was clear that quantum fields, even when they arise from the classical picture of Lagrangian functionals and actions, are more singular objects than those employed in classical physics. Their values in points of spacetime, i.e., their point-like dependence as operator-valued functions, is easily seen to clash with their realizability as operators on an Hilbert space on one hand, on the other hand it is neither dictated by physics. The structure of spacetime itself, at very small scales, is by now out of our experimental reach. In order to overcome the previous difficulties the notion of field can be relaxed to that of an (unbounded) operator-valued distribution (Wightman axiomatization), elevating the smearing with test functions to an essential feature of a local quantum theory. This generalization introduces more difficult mathematical objects (distributions, compared to functions) but which can be rigorously (without ambiguities) treated, and which are suitable enough to obtain a complete scattering theory, once a Wightman QFT is assigned. In the same spirit, but with different mathematics, QFTs can be dealt with using techniques from the theory of operator algebras. The first main characteristics of the algebraic approach (AQFT) is that one describes local measurements or observable fields and regards them as the primary objects of interest to study matter, particles and fundamental interactions, relegating the non-observable quantities to theoretical tools. Secondly, one treats them by means of bounded operators on Hilbert space (e.g., by considering bounded functions of the fields), advantageous at least for the analysis of the framework. More in details, physically relevant quantities such as observables (and states) of a QFT are described in terms of abstract operator algebras associated to open bounded regions of spacetime (“local algebras”). By abstract we mean independent of any specific Hilbert space realization, and then we regard the choice of different representations of the local algebras as the choice of different states (mathematically speaking via the GNS construction). In particular these objects encode both quantum behaviour, in their intrinsic non-commutativity, and Einstein’s causality principle, in the triviality of commutation relations between local algebras sitting at space-like distances. This second approach is what this thesis is devoted to. The relation between these two formalisms is not completely understood, from distributions to local algebras one has to take care of spectral commuta- tion relations on suitable domains, vice versa one should control the scaling limits of the local algebras in order to exploit the distributional “point-like” generators. In both cases, and (theoretically) in any other mathematically sound description of QFT, consequences become proofs, and different features of models or more general model-independent principles (particle content, covariance, local commutation relations) can be separated and analysed. Moreover, beyond the needs of rigorous description of models, the “axiomatic” approaches to QFT have the advantage of being more independent from classical analogies, like field equations and Lagrangians. Fields themselves are not an essential input to model local measurements obeying the constraints of Einstein’s special relativity and quantum theory. AQFT can be thought of as being divided into two lines, the first aims to the construction of models (either in low or high dimensions, both starting from physical counterparts or using the theory of operator algebras), the second is devoted to the analysis of the assumptions and of the possibly new mathematical structures arising from them. The work presented in this thesis has been developed and expresses its contribution in the second line of research. Our aim is to introduce new invariants for local quantum field theories, more specifically to complete a well established construction (the DHR construction) which associates a certain category of representations (collection of superselection sectors together with their fusion rules, exchange symmetry, statistics) to any local quantum field theory, once the latter is formulated as a local net of algebras.

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Hogervorst, Matthijs. "Two studies on conformal and strongly coupled quantum field theories in d>2 dimensions." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0013/document.

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Cette these examine deux aspects des theories conformes des champs (TCC) en d dimensions.Sa premiere parti est dediee aux blocs conformes, des fonctions speciales qui contribuent au developpement en ondes partielles des fonctions a quatre points dans les TCC. On montre que ces blocs admettent un developpement en coordonnees polaires dont les coecients se calculent par une recurrence. Les blocs conformes sont naturellement denis sur le plan complexe : on considere alors leur restriction a l'axe r eel, an de montrer qu'ils obeissent une equation dierentielle sur ce domaine, ce qui mene a un algorithme ecace pour calculer les blocs conformes et leurs derivees pour tout d. Quelques applications au programme de bootstrap sont developpees. La seconde partie de cette these examine les perturbations d'une TCC par des operateurs pertinents. On etudie de tels ots du groupe de renormalisation en utilisant la Methode de Troncature Conforme (MTC) de Yurov et Zamolodchikov, une methode numerique qui permet de faire des calculs non-perturbatifs en theorie quantique des champs. Deux theories derentes sont considerees : le boson libre avec un terme de masse, et la theorie 4. Pour le dernier cas, les resultats de la MTC mettent en evidence la brisure de symetrie Z2. Finalement, on developpe une methode pour reduire les erreurs de troncature en ajoutant des contre-termes a l'action \nue" de la MTC, suivant des travaux anterieurs en d = 2 dimensions
This thesis investigates two aspects of Conformal Field Theories (CFTs) in d dimensions. Its rst part is devoted to conformal blocks, special functions that arise in the partial wave expansion of CFT four-point functions. We prove that these conformal blocks admit an expansion in terms of polar coordinates and show that the expansion coecients are determined by recursion relations. Conformal blocks are naturally dened on the complex plane: we study their restriction to the real line, and show that they obey a fourth-order dierential equation there. This ODE can be used to eciently compute conformal blocks and their derivatives in general d. Several applications to the conformal bootstrap program are mentioned. The second half of this thesis investigates RG ows that are dened by perturbing a CFT by a number of relevant operators. We study such ows using the Truncated Conformal Space Approach (TCSA) of Yurov and Zamolodchikov, a numerical method that allows for controlled computations in strongly coupled QFTs. Two dierent RG ows are considered: the free scalar feld deformed by a mass term, and 4 theory. The former is used as a benchmark, in order to compare numerical TCSA results to exact predictions. TCSA results for 4 theory display spontaneous Z2 symmetry breaking at strong coupling: we study the spectrum of this theory both in the Z2-broken and preserved phase, and we compare the critical exponents governing the phase transition to known values. In a separate chapter, we show how truncation errors can be reduced by adding suitable counterterms to the bare TCSA action, following earlier work in d = 2 dimensions

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34

LO, MONACO GABRIELE. "Duality walls and three-dimensional superconformal field theories." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2020. http://hdl.handle.net/10281/257786.

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Un’importante classe di teorie 3d superconformi ammette una realizzazione in teoria delle stringhe e può essere ingegnerizzata usando configurazioni di D3, D5 ed NS5 brane, chiamate configurazioni di Hanany-Witten (HW). La dinamica a basse energie di queste teorie sono state ampiamente studiate in passato: un ruolo prominente è giocato dalla mirror symmetry, una dualità tra teorie che possiedono uguale punto fisso nell’infrarosso. Mirror symmetry può essere pensata come un’eredità dell’S-dualità in teoria di stringa. Come osservato da Gaiotto e Witten, le configurazioni di HW possono essere generalizzate aggiungendo nuovi oggetti, chiamati SL(2,Z) duality walls o S-fold. Passando attraverso questa interfaccia, il sistema subisce localmente una trasformazione SL(2,Z). Setup di HW con l’inserzione di un S-fold ammettono anche una descrizione olografica in supergravità di tipo IIB, come mostrato recentemente da Assel e Tomasiello. Da un punto di vista di teoria di campo, l’inserzione di un S-fold si manifesta come una teoria T[U(N)] in cui ogni fattore U(N) nel gruppo di simmetria U(N)x U(N) è gaugiato allo stesso tempo, generando un accoppiamento non banale tra due multipletti vettoriali. In questo senso, T[U(N)] gioca il ruolo di materia non convenzionale. Chiameremo S-fold SCFT una teoria con un accoppiamento T[U(N)] (T-link): queste teorie possono essere pensate come una generalizzazione degli usuali quiver circolari N=4. È importante sottolineare che solo un fattore U(N) del gruppo di simmetria è manifesto nella descrizione Lagrangiana di T[U(N)], mentre l’altro è emergete nell’infrarosso. Per tale motivo, un T-link aggiunge un elemento non-lagrangiano e lo studio delle teorie con S-fold risulta essere un’intrigante sfida da un punto di vista di QFT. Lo scopo di questa tesi è studiare in più dettaglio le S-fold SCFT. Ci concentreremo prevalentemente sullo spazio dei moduli, dualità e la supersimmetria preservata nell’infrarosso. Lo strumento principale per studiare lo spazio dei moduli è la mirror symmetry. Quando tutti i livelli di Chern-Simons (CS) sono spenti, proponiamo che l’Higgs branch di queste teorie può essere calcolato effettuando un hyperKahler quotient. Inoltre, congetturiamo che il Coulomb branch coincide con il Coulomb branch di un quiver effettivo dove i nodi accoppiati dal T-link sono congelati. Chiamiamo questo fenomeno freezing rule e possiamo interpretarlo come l’impossibilità di una D3 brana di muoversi in certe direzioni nel caso in cui intersechi un S-fold. Generalizziamo anche le S-fold SCFT a casi più generali dove appare una teoria T[G], con G gruppo ortogonale, simplettico o eccezionale. Nel caso di G gruppo classico, proponiamo queste teorie essere duali a configurazioni di HW in cui un S-fold convive con O-piani. In tutti i casi descritti, verifichiamo la consistenza delle nostre proposte con mirror symmetry, calcolando la serie di Hilbert dei moduli space. Nel caso di G non-abeliano e livelli di CS accesi, non siamo in grado di fornire un’unica prescrizione per calcolare il moduli space. Tuttavia, studiamo dettagliatamente i modelli abeliani. Poiché in questo caso T[U(1)] è una teoria quasi vuota contente solo un termine di CS misto, siamo in grado di calcolare il moduli space, provando così a dedurre il modo di contribuire alla dinamica di T[U(N)]. Infine, studiamo l’indice superconforme delle teorie con S-fold. Tale quantità è utile per due scopi. Il primo è studiare dualità tra teorie con S-fold descritte da quiver differenti. In tale contesto, l’indice rivela come gli operatori sono mappati tra loro sotto la dualità. Il secondo scopo è studiare la quantità di supersimmetria preservata da una teoria con S-fold nel IR. Il gauging delle simmetrie globali di T[U(N)] rompe la supersimmetria a N=3. Tuttavia, in molti esempi con N finito, l’indice mostra che la supersimmetria aumenta nell’infrarosso.
A notable class of 3d N=4 superconformal field theories admits a string theoretic realization and can be engineered using brane configurations of D3, D5 and NS5 branes, usually called Hanany-Witten (HW) configurations. The low energy dynamics of such theories have been extensively studied in the past year: a prominent role is played by mirror symmetry, a duality between theories having the same conformal fixed point in the infrared. Mirror symmetry can be thought as inherited from string theory S-duality. As observed by Gaiotto and Witten, HW setups can be generalized by adding new objects, SL(2,Z) duality walls, also called S-folds. When passing through this interface, the system undergoes a local SL(2,Z) transformation. HW setups where an S-fold inserted also admit a holographic description in Type-IIB supergravity as recently shown by Assel and Tomasiello. From a QFT side, the insertion of an S-fold manifests itself as a T[U(N)] theory where each U(N) factor in the global symmetry U(N)xU(N) is commonly gauged, thus generating a non-trivial coupling between two vector multiplets. In this sense, T[U(N)] plays the role of unconventional matter. We refer to theories where a T[U(N)]-link (or simply T-link) has been inserted as S-fold theories: they can be thought of as a generalization of usual N=4 circular quivers. It is worth to stress that only one U(N) factor of the global symmetry is manifest in the Lagrangian description of T[U(N)], whereas the other is emergent at the infrared fixed point. In this sense, a T-link adds a non-Lagrangian ingredient and studying S-fold theories turns out to be an intriguing challenge from a quantum field theory point of view. The aim of this thesis is to gain insight about S-fold SCFTs. We mainly focus on their vacuum moduli spaces, dualities and infrared supersymmetry. We study the moduli space of S-fold SCFTs using mirror symmetry as main tool. When all Chern-Simons (CS) levels are turned off, we propose that the Higgs branch of such theories can be computed performing an hyper-Kahler quotient. Moreover, we conjecture that the Coulomb branch is the same of the Coulomb branch of an effective quiver where the T-linked gauge nodes get frozen. We name this phenomenon freezing rule and we interpret as the fact impossibility of D3 branes to move in some directions when intersecting an S-duality wall. We also generalize S-fold SCFTs to more general cases where a T[G] theory appears, with G being orthogonal, symplectic as well as exceptional groups. For G a classical group, we propose that such theories are dual to HW configurations where an S-fold coexists with orientifold planes. In all these cases, we check our proposals computing the Hilbert series associated to each moduli space and checking it against mirror symmetry. When G is non-Abelian and the CS levels are turned on, we are not able to provide a unique prescription in order to compute the moduli space in presence of a T-link. Nevertheless, we study in full details a sub-class consisting of Abelian models. Since in this case T[U(1)] is an almost empty theory with only a mixed CS term, we are able to compute the moduli space, trying to infer how a T[U(N)] theory should enter the dynamics. Finally, we study the superconformal indices of S-fold theories. Such a quantity is useful for two purposes. The first one is to study the duality between S-fold theories with different quiver descriptions. In this context the index reveals how operators get mapped to each other under the duality. The second purpose is to study the amount of supersymmetry possessed by the S-fold theory at low energies. In principle, the gauging of the global symmetries of a T[U(N)] theory generically breaks supersymmetry down to N=3. However, in many examples with finite N, the index showed that supersymmetry gets enhanced in the infrared. This is also consistent with the supergravity duals, which suggest the enhancement of supersymmetry in the large N limit.

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GORINI, NICOLA. "Aspects of Quantum Field Theories in Three Dimensions." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/364292.

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In questa tesi costruiamo il settore topologico unidimensionale della teoria ABJ(M) e studiamo la sua relazione con la funzione di partizione, deformata da parametri di massa, definita sulla sfera tridimensionale. La tecnica di localizzazione supersimmetrica consente di rappresentare tale funzione di partizione come un integrale finito-dimensionale (o integrale matriciale). E\' stata proposta una congettura secondo cui le funzioni di correlazione di operatori topologici possono essere ottenute prendendo certe derivate della funzione di partizione rispetto ai parametri di massa. In questa tesi presentiamo un'evidenza non banale della correttezza della congettura, calcolando le funzioni a tre e quattro punti ad un loop e la funzione a due punti a due loop, ritrovando correttamente i risultati ottenuti prendendo le derivate dell'integrale matriciale deformato una volta espanso in regime di accoppiamento debole. In aggiunta, otteniamo l'espressione della carica centrale della teoria a due loop, generalizzando i risultati noti in letteratura. In seguito ci focalizziamo sullo studio delle fasi infrarosse di teorie tridimensionali di Chern-Simons quiver, ovvero il cui gruppo di gauge è composto da due fattori non Abeliani. Discutiamo in dettaglio i casi in cui i livelli di Chern-Simons sono uguali e il caso in cui sono opposti, proponendo alcune dualità riguardanti sia coppie di teorie quiver che teorie quiver con la versione supersimmetrica della QCD tridimensionale.
In this thesis we construct the one-dimensional topological sector of $\mathcal N = 6$ ABJ(M) theory and study its relation with the mass-deformed partition function on $\mathbb S^3$. Supersymmetric localization provides an exact representation of this partition function as a matrix integral and it has been proposed that correlation functions of certain topological operators are computed through derivatives with respect to the masses. We present non-trivial evidence for this relation by computing the three- and four- point function up to one loop and the two-point function at two loops, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product, we obtain the two-loop explicit expression for the central charge $c_T$ of ABJ(M) theory. When then shift our attention to the study of the infrared phases of two-node quiver Chern-Simons theories with minimal supersymmetry in three dimensions. We discuss both the cases of Chern-Simons levels with the same and with opposite signs, where the latter case turn out to be more non-trivial. The determination of their phase diagrams allows us to conjecture certain infrared dualities involving either two quiver theories, or a quiver and adjoint QCD$_3$.

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36

Delporte, Nicolas. "Tensor Field Theories : Renormalization and Random Geometry." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP011.

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Cette thèse se scinde en deux volets, avec vue sur la renormalisation de théorie quantique des champs.Le premier volet traite de trois modèles tensoriels en trois dimensions, un quartique fermionique de rang 3 et deux sextiques bosonique, de rangs 3 et 5. On se base sur l'expansion melonique à grand N des théories tensorielles. Pour le premier modèle, invariant sous le groupe U(N)³, on calcule le flot du groupe de renormalisation des deux couplages meloniques et on dresse le diagramme des phases du vide de la théorie, en étudiant sa reformulation par un champ intermédiaire matriciel diagonalisable. Observant une brisure spontanée de la symétrie discrète chirale, la comparaison avec le modèle de Gross-Neveu tri-dimensionel est faite. Au-delà de la phase symétrique U(N)³ sans masse, on note aussi une phase massive de même symétrie et une autre où la symétrie est brisée vers U(N²) x U(N/2) x U(N/2). Un modèle matriciel de symétrie U(N) x U(N²), présentant les mêmes caractéristiques, est aussi considéré.Dans les deux autres modèles tensoriels, de groupes de symétrie U(N)³ et O(N)⁵, un couplage non-melonique (la ``roue") adjoint d'une puissance de N optimale nous conduit à une expansion melonique généralisée. Les termes cinétiques sont pris de courte ou longue portée et on étudie, à grand N, perturbativement les différents groupes de renormalisation des couplages d'ordre 6, jusqu'à quatre boucles. Tandis que le modèle de rang 5 ne présente pas de point fixe non-trivial, celui de rang 3 possède deux points fixes non-triviaux réels de type Wilson-Fisher dans le cas à courte portée et une ligne de points fixes dans l'autre. On obtient enfin les dimensions conformes réelles des opérateurs primaires bilinéaires en le champ fondamental.Le second volet établit les premiers résultats de renormalisation constructive multi-échelle pour un modèle scalaire quartique sur des arbres de Galton-Watson critiques, avec un terme cinétique à longue portée. Au point critique, l'émergence d'une spine infinie fournit un espace de dimension effective 4/3 sur lequel calculer des fonctions de corrélations moyennées. Cela formalise la notion de théorie des champs sur une géométrie aléatoire. Nous utilisons dans notre approche des bornes probabilistes sur le noyau de la chaleur dans un graphe aléatoire. On esquisse pour terminer l'extension du formalisme à des fermions et à une spine compactifiée
This thesis divides into two parts, focusing on the renormalization of quantum field theories. The first part considers three tensor models in three dimensions, a fermionic quartic with tensors of rank-3 and two bosonic sextic, of ranks 3 and 5. We rely upon the large-N melonic expansion of tensor models. For the first model, invariant under U(N)³, we compute the renormalization group flow of the two melonic couplings and establish the vacuum phase diagram, from a reformulation with a diagonalizable matrix intermediate field. Noting a spontaneous symmetry breaking of the discrete chiral symmetry, the comparison with the three-dimensional Gross-Neveu model is made. Beyond the massless U(N)³ symmetric phase, we also observe a massive phase of same symmetry and another where the symmetry breaks into U(N²) x U(N/2) x U(N/2). A matrix model invariant under U(N) x U(N²), sharing the same properties, is also studied.For the two other tensor models, with symmetry groups U(N)³ and O(N)⁵, a non-melonic coupling (the ``wheel") with an optimal scaling in N drives us to a generalized melonic expansion. The kinetic terms are taken of short and long range, and we analyze perturbatively, at large-N, the renormalization group flows of the sextic couplings up to four loops. While the rank-5 model doesn't present any non-trivial fixed point, that of rank 3 displays two real non-trivial Wilson-Fisher fixed points in the short-range case and a line of fixed points in the other. We finally obtain the real conformal dimensions of the primary operators bilinear in the fundamental field.In the second part, we establish the first results of constructive multi-scale renormalization for a quartic scalar field on critical Galton-Watson trees, with a long-range kinetic term. At the critical point, an emergent infinite spine provides a space of effective dimension 4/3 on which to compute averaged correlation fonctions. This approach formalizes the notion of a quantum field theory on a random geometry. We use known probabilistic bounds on the heat-kernel on a random graph. At the end, we sketch the extension of the formalism to fermions and to a compactified spine

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37

ROTA, ANDREA. "Holography for six dimensional theories: a universal framework." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/94885.

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It is challenging to define higher dimensional quantum field theories. For example, a Lagrangian description is often lacking. Moreover, gauge theories are non renormalizable in d > 4. A possible ultraviolet completion is string theory, which is a natural arena for the study of many interesting field theories. In particular, string theory provides us with a powerful tool for the study of conformal field theories: the AdS/CFT correspondence. The AdS/CFT is a duality that relates a theory of quantum gravity in Anti de Sitter space in (p+2)-dimensions to a conformal field theory in (p+1)-dimensions, an explicit realization of the so called holographic principle which is possible thanks to the presence of Dp-branes. These are p-dimensional objects that act as sources of gravity, carrying a (p+1)-dimensional gauge theory on their world volume. In the so called decoupling limit, the gauge degrees of freedom living on the brane decouple from gravity, which results in a AdS(p+2) vacuum state. In this thesis we use holography to study six dimensional theories. In particular we consider the so called (1, 0) conformal field theories, which are the half supersymmetric cousins of the more popular (2,0) theories living on M5 branes, whose gravity dual is the maximally supersymmetric vacuum AdS7 × S4 of M-theory. The simplest example of (1, 0) theory can be obtained orbifolding this solution. More general (1, 0) theories can be constructed in the AdS/CFT setup via brane configurations involving NS5, D6 and D8 branes. In the decoupling limit these configurations give rise to AdS7 vacua in massive type IIA supergravity. We give a complete classification of these vacua, with an infinite class of analytic solutions that correspond to infinite possible configurations of branes. The resulting internal space M3 has the topology of a three sphere, with SU(2) isometry and physical singularities at the points where the branes are located. We also classify all possible compactifications of these solutions, obtained wrapping the branes on two, three and four-manifolds of negative curvature, leading to AdS5, AdS4 and AdS3 vacua. Complete flows connecting AdS7 to the lower dimensional vacua can be constructed, suggesting the existence of a renormalization group flow between the six dimensional CFT at high energies and a lower dimensional CFT in four, three, two-dimensions at low energies. Even though these lower dimensional theories are not yet known, they now have a holographic description. The AdS4 solutions are also interesting as four-dimensional vacua with localized sources. The compactification procedure is so universal it suggests to consider a complete reduction ansatz of type IIA supergravity on the internal space M3. Indeed, the dimensional reduction leads to minimal gauged supergravity in seven dimensions, a theory with sixteen supercharges and an SU(2) gauge field. This reduction procedure does not depend on the details of the internal space M3 and thereby on the particular choice of brane configuration. We can thus claim to have a universal consistent truncation for 6d/7d gauge/gravity duals.

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38

Kukhtina, Antonia Mitkova [Verfasser], Karl-Henning [Akademischer Betreuer] Rehren, Stefan [Akademischer Betreuer] Hollands, and Laura [Akademischer Betreuer] Covi. "Local Extensions of Completely Rational Conformal Quantum Field Theories / Antonia Mitkova Kukhtina. Gutachter: Karl-Henning Rehren ; Stefan Hollands ; Laura Covi. Betreuer: Karl-Henning Rehren." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2011. http://d-nb.info/1043609636/34.

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39

Söderberg, Alexander. "Anomalous Dimensions in the WF O(N) Model with a Monodromy Line Defect." Thesis, Uppsala universitet, Teoretisk fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-317546.

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General ideas in the conformal bootstrap program are covered. Both numerical and analytical approaches to the bootstrap equation are reviewed to show how it can be manipulated in different ways. Further analytical approaches are studied for theories with defects. We consider the three-dimensional CFT at the corresponding WF fixed point in the O(N) \phi^4 model with a co-dimension two, monodromy defect. Anomalous dimensions for bulk- and defect-local fields as well as one of the OPE coefficients are found to the first loop order. Implications of inserting this defect and constraints that arises from symmetries of the theory are investigated.

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40

Longino, Brando. "Exact S-matrices for a class of 1+1-dimensional integrable factorized scattering theories with Uq(sl2) symmetry and arbitrary spins." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20542/.

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In this thesis we will study the S-matrices associated to a new class of (1+1)-dimensional integrable models with Uq(sl2) symmetry, whose asymptotic particle states organize into a k/2 isospin multiplet, with k= 0,1,2,... Such S-matrices generalize the case study previously analyzed by S. R. Aladim and M. J. Martins, where it was only investigated the non-deformed limit q→1 of pure SU(2) symmetry. We check that the proposed S-matrix satisfies the constraints due to the the Yang-Baxter equation, crossing-symmetry requirement and unitarity and therefore defines a self-consistent integrable factorized scattering theory.

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41

Giorgetti, Luca [Verfasser], Karl-Henning [Akademischer Betreuer] Rehren, Dorothea [Gutachter] Bahns, Roberto [Gutachter] Longo, Laura [Gutachter] Covi, Stefan [Gutachter] Kehrein, and Ralf [Gutachter] Meyer. "Braided Actions of DHR Categories and Reconstruction of Chiral Conformal Field Theories / Luca Giorgetti ; Gutachter: Dorothea Bahns, Roberto Longo, Laura Covi, Stefan Kehrein, Ralf Meyer ; Betreuer: Karl-Henning Rehren." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2016. http://d-nb.info/1116709848/34.

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42

Giorgetti, Luca Verfasser], Karl-Henning [Akademischer Betreuer] Rehren, Dorothea [Gutachter] Bahns, Roberto [Gutachter] Longo, Laura [Gutachter] Covi, Stefan [Gutachter] [Kehrein, and Ralf [Gutachter] Meyer. "Braided Actions of DHR Categories and Reconstruction of Chiral Conformal Field Theories / Luca Giorgetti ; Gutachter: Dorothea Bahns, Roberto Longo, Laura Covi, Stefan Kehrein, Ralf Meyer ; Betreuer: Karl-Henning Rehren." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2016. http://d-nb.info/1116709848/34.

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43

Schuster, Theodor. "Scattering amplitudes in four- and six-dimensional gauge theories." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2014. http://dx.doi.org/10.18452/17034.

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Streuamplituden der Quantenchromodynamik (QCD), N = 4 Super-Yang-Mills-Theorie (SYM-Theorie) und der sechsdimensionalen N = (1, 1) SYM-Theorie werden untersucht, mit einem Fokus auf die Symmetrien und Relationen zwischen den Streuamplituden dieser Eichtheorien auf dem Baum-Niveau. Die Baum-Niveau- und Ein-Schleifen-Farbzerlegung beliebiger QCD-Amplituden in primitive Amplituden wird bestimmt und Identitäten hergeleitet, welche den Nullraum unter den primitiven Amplituden aufspannen. Anschließend wird bewiesen, dass alle farbgeordneten Baum-Niveau-Amplituden der masselosen QCD aus der N = 4 SYM-Theorie erhalten werden können. Analytische Formeln für alle für die QCD relevanten N = 4 SYM-Amplituden werden bestimmt und die Effizienz und Genauigkeit der numerischen Auswertung der analytischen Formeln für farbgeordnete QCD-Baum-Niveau-Amplituden mit einer effizienten numerischen Implementierung der Berends-Giele-Rekursion verglichen. Die Symmetrien der massive Amplituden auf dem Coulomb-Zweig der N = 4 SYM-Theorie werden hergeleitet. Diese können durch eine dimensionale Reduktion der masselosen Baum-Niveau-Amplituden der sechsdimensionalen N = (1, 1) SYM-Theory erhalten werden. Darüber hinaus wird bezeigt, wie es mit Hilfe einer numerischen Implementierung der BCFW-Rekursion möglich ist analytische Formeln für die Baum-Niveau-Superamplituden der N = (1, 1) SYM-Theory zu erhalten und die Möglichkeit eines Uplifts der masselose Baum-Niveau-Amplituden der N = 4 SYM-Theory untersucht. Schließlich wird eine Alternative zur dimensionalen Regularisierung der N = 4 SYM-Theorie untersucht. Die Infrarotdivergenzen werden hierbei durch Massen regularisiert, die durch einen Higgs-Mechanismus erhalten wurden. Die korrespondierende Stringtheorie-Beschreibung deutet auf eine exakte duale konforme Symmetrie der Streuamplituden hin. Durch explizite Rechnungen wird dies bestätigt und Vorteile des Regulators werden demonstriert.
We study scattering amplitudes in quantum chromodynamics (QCD), N = 4 super Yang-Mills (SYM) theory and the six-dimensional N = (1, 1) SYM theory, focusing on the symmetries of and relations between the tree-level scattering amplitudes in these three gauge theories. We derive the tree level and one-loop color decomposition of an arbitrary QCD amplitude into primitive amplitudes. Furthermore, we derive identities spanning the null space among the primitive amplitudes. We prove that every color ordered tree amplitude of massless QCD can be obtained from gluon-gluino amplitudes of N = 4 SYM theory. Furthermore, we derive analytical formulae for all gluon-gluino amplitudes relevant for QCD. We compare the numerical efficiency and accuracy of evaluating these closed analytic formulae for color ordered QCD tree amplitudes to a numerically efficient implementation of the Berends-Giele recursion. We derive the symmetries of massive tree amplitudes on the coulomb branch of N = 4 SYM theory, which in turn can be obtained from N = (1, 1) SYM theory by dimensional reduction. Furthermore, we investigate the tree amplitudes of N = (1, 1) SYM theory and explain how analytical formulae can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation and investigate a potential uplift of the massless tree amplitudes of N = 4 SYM theory. Finally we study an alternative to dimensional regularization of N = 4 SYM theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. We confirm this expectation and illustrate the calculational advantages of the massive regulator by explicit calculations.

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44

Broccoli, Matteo. "On the trace anomaly of a Weyl fermion in a gauge background." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/16408/.

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In this thesis we study the trace anomaly of a Weyl fermion in an abelian gauge background. We first introduce the topic of anomaly in Quantum Fields Theory and provide case studies of a global and a gauge anomaly. Then, we review the lagrangians of the Weyl fermion and Dirac fermion, the models that are the focus of our chiral and trace anomaly computations. Since we evaluate the anomalies using Pauli-Villars (PV) regularization, we present different PV masses and discuss the classical symmetries they break. We identify the differential operators that enter our regularization schemes and we review the method that we use to evaluate anomalies: we read them from the path integral à la Fujikawa and compute them with heat kernel formulas. Then, we evaluate the chiral and trace anomaly of the models we are interested in. The chiral anomaly is well studied in the literature and we reproduce the standard result. The trace anomaly is our original result and, although the presence of the chiral anomaly implies a breakdown of gauge invariance, we find that the trace anomaly can be cast in a gauge invariant form. The issue is analogous to the one recently discussed in the literature about a conjectured contribution of an odd-parity term to the trace anomaly of a Weyl fermion in curved backgrounds. With an abelian gauge background, this odd-parity term would be a Chern-Pontryagin density, that does not appear in our final results.

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45

Bonansea, Sara. "Wilson loops at weak and strong coupling in N = 4 Super Yang-Mills with defects." Doctoral thesis, 2020. http://hdl.handle.net/2158/1217895.

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This PhD thesis is devoted to the study of circular Wilson loops in a defect version of N=4 super-Yang-Mills theory which is dual to the D5-D3 brane system. When the loops are parallel to the defect, we can construct both BPS and non-BPS operators. At strong 't Hooft coupling we observe, in the non-BPS case, a Gross-Ooguri-like phase transition in the dual gravitational theory: the familiar disk solution dominates when the operator is far from the defect while a cylindrical string worldsheet, connecting the boundary loop with the probe D5-brane, is favorite below a certain distance. In the BPS case, the cylindrical solution does not exist for any choice of the physical parameters, suggesting that light-modes supergravity exchanges with the disk solution always saturate the expectation value at strong coupling. We study the double-scaling limit for large k and large 't Hooft coupling that allows us to compare perturbative and non-perturbative results. In the last chapter, we study the case in which two concentric circular Wilson loops are inserted in the defect theory.

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46

Wapler, Matthias Christian. "Holographic Experiments on Defects." Thesis, 2009. http://hdl.handle.net/10012/4688.

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Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

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47

Trevisani, Emilio. "Bootstrapping conformal field theories." Doctoral thesis, 2017. https://repositorio-aberto.up.pt/handle/10216/105115.

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48

Trevisani, Emilio. "Bootstrapping conformal field theories." Tese, 2017. https://repositorio-aberto.up.pt/handle/10216/105115.

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49

Bertolini, Marco. "Moduli Space of (0,2) Conformal Field Theories." Diss., 2016. http://hdl.handle.net/10161/12834.

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In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Dissertation

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50

Raju, Avinash. "Aspects of Higher Spin Theories Conformal Field Theories and Holography." Thesis, 2017. http://etd.iisc.ernet.in/2005/3643.

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This dissertation consist of three parts. The first part of the thesis is devoted to the study of gravity and higher spin gauge theories in 2+1 dimensions. We construct cosmological so-lutions of higher spin gravity in 2+1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary CFT partition function, and reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using a prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS3. For the case of negative cosmological constant we show that interpreting the inverse AdS3 radius 1=l as a Grassmann variable results in a formal map from gravity in AdS3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS3 case. Our results straightforwardly generalize to the higher spin case: the flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We also demonstrate the power of our approach by doing singularity resolution in the BMS gauge as an application. Finally, we construct a candidate for the most general chiral higher spin theory with AdS3 boundary conditions. In the Chern-Simons language, the left-moving solution has Drinfeld-Sokolov reduced form, but on the right-moving solution all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are 19 functions. Despite this, we show that the resulting metric has the form of the “most general” AdS3 boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a W3 algebra on the left and an affine sl(3)k current algebra on the right, as desired. The metric and higher spin fields depend on all the 19 functions. The second part is devoted to the problem of Neumann boundary condition in Einstein’s gravity. The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions. In our work, we view Neumann boundary condition not as fixing the normal derivative of the metric (“velocity”) at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric (“momentum”). This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient. In three dimensions this boundary term reduces to a “one-half” GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms. In four dimensions the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We also argue that a natural boundary condition for gravity in asymptotically AdS spaces is to hold the renormalized boundary stress tensor density fixed, instead of the boundary metric. This leads to a well-defined variational problem, as well as new counter-terms and a finite on-shell action. We elaborate this in various (even and odd) dimensions in the language of holographic renormalization. Even though the form of the new renormalized action is distinct from the standard one, once the cut-off is taken to infinity, their values on classical solutions coincide when the trace anomaly vanishes. For AdS4, we compute the ADM form of this renormalized action and show in detail how the correct thermodynamics of Kerr-AdS black holes emerge. We comment on the possibility of a consistent quantization with our boundary conditions when the boundary is dynamical, and make a connection to the results of Compere and Marolf. The difference between our approach and microcanonical-like ensembles in standard AdS/CFT is emphasized. In the third part of the dissertation, we use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the O(N) Gross-Neveu model in d = 2 + dimensions. To do this, we extend the “cow-pie contraction” algorithm of Basu and Krishnan to theories with fermions. Our results match perfectly with Feynman diagram computations.

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Дисертації з теми "Defect Conformal Field Theories"

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