Thèses : « Supersymmetric field theorie »

1

MAURI, ANDREA. « On marginal deformations of N = 4 super Yang–Mills theory ». Doctoral thesis, Universita' degli Studi di Milano, 2008. http://hdl.handle.net/10281/125449.

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In this Thesis I analyze some aspects of a class of quantum field theories that can be obtained by marginally deforming N=4 SYM theory. These theories constitue a very non trivial example of N=1 superconformal actions in four dimensional space-time and play a role in the context of AdS/CFT. I begin by introducing superfield notations and constructing deformed theories following Leigh and Strassler procedure. Then an analysis of the finiteness properties of the actions is performed. Considering different specific cases, solutions of the superconformal constraint are given. The issues of conformal invariance and finiteness in the case of complex and real beta-deformed models are addressed. In the real beta case an all loop solution of the constraint is provided. In the case of complex deformation, it turns out that the condition of vanishing beta function leads to a result which is scheme dependent. In the second part of the work, anomalous dimensions of composite operators are computed. A new method for extracting protected operators in the chiral sector is introduced. Using the proposed procedure it is possible to gain a loop order in perturbative computations with respect to canonical methods. The structure of the chiral ring of the deformed theories is then classified up to three loops.

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Goodyear, Stephen Geoffrey. « Lattice and supersymmetric field theories ». Thesis, University of Edinburgh, 1985. http://hdl.handle.net/1842/12044.

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Sämann, Christian. « Aspects of twistor geometry and supersymmetric field theories within superstring theory ». [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=979814936.

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4

Hartley, David. « Supersymmetric quantum field theories from induced representations ». Thesis, University of St Andrews, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329888.

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5

Kingaby, Thomas. « Exact results in supersymmetric field theory ». Thesis, Swansea University, 2003. https://cronfa.swan.ac.uk/Record/cronfa42267.

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This thesis examines N = 2 Super-Yang-Mills theory where the low-energy effective action of the theory is governed by a holomorphic function called the prepotential. The Seiberg-Witten solution of the theory determines the prepotential in terms of an complex curve and, once we compactify the theory on a circle, we will examine the identification of this complex curve with the spectral curve of the Calogero-Moser integrable system. Since the supersymmetry restricts the perturbative contributions to the prepotential, the results we gain are exact. Further, they are independent of the compactification radius. The generalization to the quiver models, with gauge group SU(N)k, is introduced along with the spin generalization of the integrable system. The massive vacua of these theories have been determined previously, here we examine the case of a specific gauge group in order to determine the complete phase structure, including the massless vacua. We then move on to determining contributions coming from instantons to the prepotential of the theory with gauge group SU(N). We see how by lifting the theory onto 5 dimensions the functional integral on the instanton moduli space is realized as a quantum mechanical sigma-model with the moduli space as a target. However, just such a model is shown to calculate a particular index of the manifold, in this case a particular equivariant index since the space has isometries. We account for the non-compact nature of the moduli space by removing boundary terms and then calculate explicit results in the case of SU(2).

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Zhao, Peng. « Integrability in supersymmetric gauge theories ». Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648125.

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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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Galloni, Daniele Stefano. « Supersymmetric field theories, scattering amplitudes and the Grassmannian ». Thesis, Durham University, 2015. http://etheses.dur.ac.uk/11129/.

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In this thesis we carry out a detailed investigation of a class of four-dimensional N=1 gauge theories, known as Bipartite Field Theories (BFTs), and their utility in integrable systems and scattering amplitudes in 4-dimensional N=4 Super-Yang-Mills (SYM). We present powerful combinatorial tools for analyzing the moduli spaces of BFTs, and find an interesting connection with the matching and matroid polytopes, which play a central role in the understanding of the Grassmannian. We use the tools from BFTs to construct (0+1)-dimensional cluster integrable systems, and propose a way of obtaining (1+1)- and (2+1)-dimensional integrable field theories. Using the matching and matroid polytopes of BFTs, we analyze the singularity structure of planar and non-planar on-shell diagrams, which are central to modern developments of scattering amplitudes in N=4 SYM. In so doing, we uncover a new way of obtaining the positroid stratication of the Grassmannian. We use tools from BFTs to understand the boundary structure of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory. We provide the most comprehensive study of the geometry of the amplituhedron to date. We also present a detailed study of non-planar on-shell diagrams, constructing the on-shell form using two new, independent methods: a non-planar boundary measurement valid for arbitrary non-planar graphs, and a proposal for a combinatorial method to determine the on-shell form directly from the graph.

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9

Petunin, Kirill. « Wall-crossing in supersymmetric gauge theories ». Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610005.

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Lavdas, Ioannis. « AdS₄/CFT₃ and quantum gravity ». Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE041.

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Dans le cadre de la dualité holographique entre une vaste famille de vides 1/2-maximalement supersymétriques Anti-de Sitter à quatre dimensions (AdS₄) et des théories des champs superconformes N=4 supersymétriques à trois dimensions (sCFT₃), nous étudions des questions théoriques majeures de gravité quantique et de théories de jauge. Ce travail a deux directions principales : La premiere partie est consacrée aux mécanismes par lesquels le graviton AdS₄ peut acquérir une petite masse, tandis que la seconde partie concerne la cartographie de la variété superconforme des sCFT₃ considérées. En ce qui concerne la question du mecanisme de Higgs pour le graviton d’AdS₄, nous proposons un nouveau mécanisme qui repose sur le couplage ”faible” de deux sCFT₃s, initialement découplées, en jaugent une symmétrie globale commune. Les deux tenseurs de stress initialement conservés se mélangent et le résultat est une combinaison conservée et une combinaison orthogonale, dont la dimension acquiert une petite dimension anormale. Holographiquement, cette configuration correspond à la connexion de deux univers AdS₄ initialement découplés via un AdS₅ × S⁵ fin, autrement appelé une “gorge” de Janus. Le résultat est une théorie AdS₄-bimétrique, avec un graviton sans masse et un graviton massif, dont la petite masse correspond à la dimension anormale de la combinaison duale de tenseurs de stress. Nous calculons la masse du graviton, qui est exprimée en termes de données géométriques de la ”gorge” de Janus et de l’univers AdS₄ vers zéro, résulte en une théorie de gravité massive dans AdS₄. En ce qui concerne la deuxième direction de ce travail, les déformations superconformes des sCFT₃s considérées qui génèrent la variété superconformale sont des déformations préservant N = 2 supersymétrie, générées par des opérateurs exactement marginaux. Nous présentons comment tous ces opérateurs peuvent être systématiquement extraits de l’index superconforme. Les opérateurs de branche de Coulomb et de Higgs sont pris en compte, tandis qu’une attention particuli ère est accordée aux opérateurs mixtes. On montre que les modules de branches mixtes de ces théories sont des opérateurs à double-corde qui se transforment dans la représentation (Adj, Adj) des groupes de saveursélectriques et magnétiques, modulo un surcomptage pour les quivers avec des noeuds de jauge abéliens. Enfin, nous commentons sur l’interprétation holographique des résultats, en affirmant que les supergravités mesurées peuvent capturer l’espace des modules tout entier si, outre les paramètres de la solution d’arri ère-plan, les modules de quantification des conditions aux limites sontégalement pris en compte
Based on the holographic duality between a large class of half-maximally supersymmetric four-dimensional Anti-de Sitter (AdS₄) vacua and three-dimensional N = 4 superconformal field theories (sCFT₃), we study quantum gravitational and gauge theoretic questions. This work has two main directions: The first part is devoted to the mechanisms through which the low-lying AdS₄-graviton can acquire a small mass whereas the second part regards the mapping of the superconformal manifold of the considered sCFT₃s. Regarding the question of the graviton Higgsing in AdS₄, we propose a new mechanism which relies on ”weakly” coupling two initially decoupled sCFT₃s, by gauging a common global symmetry. The two initially conserved stress tensors mix and the result of this mixing is a conserved combination and an orthogonal combination, the scaling dimension of which acquires a small anomalous dimension. Holographically, this setup is dual to connecting two initially decoupled AdS₄ universes via a thin AdS₅ × S⁵ or Janus ”throat”. The result is an AdS₄- bimetric theory, with one massless and one massive graviton, the small mass of which corresponds to the anomalous dimension of the dual stress tensor combination. We compute the mass of the graviton, which is expressed in terms of the geometric data of the Janus ”throat” and of the considered AdS₄ universe. A special decoupling limit of this theory, where the effective four-dimensional gravitational coupling of one of the two universes vanishes, results to an AdS₄-Massive gravity theory. Regarding the second direction of this work, superconformal deformations of the considered sCFT3s which generate the superconformal manifold, are N = 2 supersymmetry preserving deformations, generated by exactly marginal operators. We present how all these operators can be consistently extracted from the superconformal index. Coulomb and Higgs branch operators are considered, while particular attention is payed to mixedbranch operators. It is shown that the mixed-branch moduli of these theories are double-string operators transforming in the (Adj,Adj) representation of the electric and magnetic flavour groups, up to overcounting for quivers with abelian gauge nodes. Finally, we comment on the holographic interpretation of the results, arguing that gauged supergravities can capture the entire moduli space if, in addition to the parameters of the background solution, quantization moduli of boundary conditions are also taken into account

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Brown, William Elvis. « The development of non-perturbative methods for supersymmetric and non-supersymmetric quantum field theories ». Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244546.

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12

Davies, N. Michael. « Semiclassical monopole calculations in supersymmetric gauge theories ». Thesis, Durham University, 2000. http://etheses.dur.ac.uk/4360/.

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We investigate semiclassical contributions to correlation functions in N = 1 supersymmetric gauge theories. Our principal example is the gluino condensate, which signals the breaking of chiral symmetry, and should be exactly calculable, according to a persymmetric non-renormalisation theorem. However, the two calculational approaches previously employed, SCI and WCI methods, yield different values of the gluino condensate. We describe work undertaken to resolve this discrepancy, involving a new type of calculation in which the space is changed from R(^4) to the cylinder R(3) x S(1) This brings control over the coupling, and supersymmetry ensures that we are able to continue to large radii and extract answers relevant to R(^4). The dominant semiclassical configurations on the cylinder are all possible combinations of various types of fundamental monopoles. One specific combination is a periodic instanton, so monopoles are the analogue of the instanton partons that have been conjectured to be important at strong coupling. Other combinations provide significant contributions that are neglected in the SCI approach. Monopoles are shown to generate a superpotential that determines the quantum vacuum, where the theory is confining. The gluino condensate is calculated by summing the direct contributions from all fundamental monopoles. It is found to be in agreement with the WCI result for any classical gauge group, whereas the values for the exceptional groups have not been calculated before. The ADS superpotential, which describes the low energy dynamics of matter in a supersymmetric gauge theory, is derived using monopoles for all cases where instantons do not contribute. We report on progress made towards a two monopole calculation, in an attempt to quantify the missed contributions of the SCI method. Unfortunately, this eventually proved too complicated to be feasible.

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Brödel, Johannes [Verfasser]. « Alternative approaches to maximally supersymmetric field theories / Johannes Brödel ». Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover, 2010. http://d-nb.info/1008409782/34.

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14

Ehrhardt, Mathieu. « Indices for supersymmetric quantum field theories in four dimensions ». Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/274322.

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In this thesis, we investigate four dimensional supersymmetric indices. The motivation for studying such objects lies in the physics of Seiberg's electric-magnetic duality in supersymmetric field theories. In the first chapter, we first define the index and underline its cohomological nature, before giving a first computation based on representation theory of free superconformal field theories. After listing all representations of the superconformal algebra based on shortening conditions, we compute the associated Verma module characters, from which we can extract the index in the appropriate limit. This approach only provides us with the free field theory limit for the index and does not account for the values of the $R$-charges away from free field theories. To circumvent this limitation, we then study a theory on $\mathbb{R}\times S^3$ which allows for a computation of the superconformal index for multiplets with non-canonical $R$-charges. We expand the fields in harmonics and canonically quantise the theory to analyse the set of quantum states, identifying the ones that contribute to the index. To go beyond free field theory on $\mathbb{R}\times S^3$, we then use the localisation principle to compute the index exactly in an interacting theory, regardless of the value of the coupling constant. We then show that the index is independent of a particular geometric deformation of the underlying manifold, by squashing the sphere. In the final chapter, we show how the matching of the index can be used in the large $N$ limit to identify the $R$-charges for all fields of the electric-magnetic theories of the canonical Seiberg duality. We then conclude by outlining potential further work.

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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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Gracey, John Arthur. « Non-perturbative aspects of supersymmetric quantum field theory ». Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328667.

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Koschade, Daniel. « Aspects of supersymmetric field theories in four and six dimensions ». Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/2423.

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Supersymmetry is an important concept in modern high energy physics. It has found many applications in theoretical considerations of supersymmetric gauge theories as well as in phenomenological approaches to physics beyond the Standard Model. In this report we discuss some recent progress in supersymmetric eld theories in four and six dimensions. After introducing basic ideas and properties of supersymmetry we review the concept of scattering amplitudes in maximally supersymmetric theories in four dimensions before constructing a related framework in six dimensions. Here, the spinor helicity formalism and on-shell superspace were recently developed for six-dimensional gauge theories with (1,1) supersymmetry. We combine these two techniques with (generalised) unitarity, which is a powerful technique to calculate scattering amplitudes in any massless theory. As an application we calculate one-loop superamplitudes with four and ve external particles in the (1,1) theory and perform several consistency checks on our results. Within the area of phenomenological applications of supersymmetric gauge theories, we brie y review basic properties of supersymmetry breaking and gauge mediation in four dimensions. An important recent development has been the concept of theories with broken supersymmetry and metastable vacua. By using the advances of Seiberg duality, we examine a metastable N = 1 Macroscopic SO(N) SQCD model of Intriligator, Seiberg and Shih (ISS). We introduce various baryon and meson deformations, including multitrace operators. In this setup, direct fundamental messengers and the symmetric pseudomodulus messenger mediate supersymmetry breaking to a minimal supersymmetric Standard Model. We compute gaugino and sfermion masses and compare them for each deformation type. We also explore reducing the rank of the magnetic

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Wu, Ruoxu. « Notes on Some (0,2) Supersymmetric Theories in Two Dimensions ». Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77921.

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This thesis is devoted to a discussion of two-dimensional theories with (0,2) supersymmetry. Examples of two-dimensional (0,2) gauged linear sigma models (GLSMs) are constructed for various spaces including Grassmannians, complete intersections in Grassmannians, and non-complete intersections such as Pfaffians. Generalizations of (2,2) Toda dual theories to (0,2) Toda-like theories are also discussed and some examples are given, including products of projective spaces and del Pezzo surfaces. Correlation functions are computed to show the examples are the correct mirror models.
Ph. D.

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Nedelin, Anton. « Exact Results in Five-Dimensional Gauge Theories : On Supersymmetry, Localization and Matrix Models ». Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-243320.

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Gauge theories are one of the corner stones of modern theoretical physics. They describe the nature of all fundamental interactions and have been applied in multiple branches of physics. The most challenging problem of gauge theories, which has not been solved yet, is their strong coupling dynamics. A class of gauge theories that admits simplifications allowing to deal with the strong coupling regime are supersymmetric ones. For example, recently proposed method of supersymmetric localization allows to reduce expectation values of supersymmetric observables, expressed through the path integral, to finite-dimensional matrix integral. The last one is usually easier to deal with compared to the original infinite-dimensional integral. This thesis deals with the matrix models obtained from the localization of different 5D gauge theories. The focus of our study is N=1 super Yang-Mills theory with different matter content as well as N=1 Chern-Simons-Matter theory with adjoint hypermultiplets. Both theories are considered on the five-spheres. We make use of the saddle-point approximation of the matrix integrals, obtained from localization, to evaluate expectation values of different observables in these theories. This approximation corresponds to the large-N limit of the localized gauge theory. We derive $N^{3}$ behavior for the free energy of 5D N=1* super Yang-Mills theory at strong coupling. This result is important in light of the relation between 5D theory and the world-volume theories of M5-branes, playing a significant role in string theory. We have also explored rich phase structure of 5D SU(N) N=1 super Yang-Mills theory coupled to massive matter in different representations of the gauge group. We have shown that in the case of the massive adjoint hypermultiplet theory undergoes infinite chain of the third order phase transitions while interpolating between weak and strong coupling in the decompactification limit. Finally, we obtain several interesting results for 5D Chern-Simons theory, suggesting existence of the holographic duals to this theory. In particular, we derive $N^{5/2}$ behavior of the free energy of this theory, which reproduces the behavior of the free energy for 5D theories with known holographic duals.

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Endres, Michael G. « Topics in lattice field theory / ». Thesis, Connect to this title online ; UW restricted, 2007. http://hdl.handle.net/1773/9713.

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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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22

Wens, Vincent. « Of N=1 supersymmetric gauge theories and localization ». Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210272.

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In this thesis, we study certain non-perturbative aspects of N=1 gauge theories. We show how to compute the expectation values of chiral operators (i.e. those that preserve the anti-chiral supercharges) exactly from a first-principle approach based on the path integral over the microscopic fields.

The text is divided into two parts. The first one consists of an original introduction to the tools that underlie the researches and results obtained during this thesis. After a general introduction, we present some methods to obtain exact results. Covered topics include instantons, N=2 supersymmetry and localization,N=1 supersymmetry and holomorphy, and finally the Dijgraaf-Vafa matrix model formalism and the perturbative generalized Konishi anomaly equations. These preliminaries were chosen to enlighten the presentation of our results. A brief overview of our results is then. This includes localization in some N=1 gauge theories, its applications to the computation of chiral correlators as well as a non-perturbative discussion of the generalized Konishi equations and of the Dijkgraaf-Vafa glueball superpotential. We insist on the ideas and the results, postponing the details for the second part, which consists of a faithful reproduction of the papers published during this thesis and in which the author has been involved. /

Dans cette thèse, nous étudions certains aspects non-perturbatifs des théories de jauge supersymétriques N=1. Plus précisemment, nous montrons comment les valeurs moyennes des opérateurs chiraux (qui préservent la moitié des supercharges) dans les vides quantiques peuvent être calculées sans approximations, à partir d'une approche basée sur l'intégrale fonctionnelle sur les champs microscopiques.

Ce mémoire est divisé en deux parties. La première consiste en une introduction à l'approche microscopique des théories de jauge supersymétriques. Une grande fraction de celle-ci est dédiée à la présentation des concepts et méthodes qui sont à la base du développement de ce formalisme et de nos recherches. Ceci inclut les instantons, la supersymétrie N=2 et la localisation dans l'intégrale fonctionnelle, la supersymétrie N=1 et l'holomorphie, et enfin l'approche de Dijkgraaf-Vafa basée sur un modèle de matrices et les équations d'anomalie généralisées de Konishi. Ensuite, nous présentons le formalisme microscopique et les résultats obtenus durant cette thèse. Nous expliquons comment utiliser la technique de localisation dans certaines théories de jauge N=1 et comment l'appliquer au calcul des valeurs moyennes des opérateurs chiraux. Nous discutons également de façon non-perturbative les équations d'anomalie généralisées de Konishi et le superpotentiel de Dijkgraaf-Vafa. La plupart des résultats exacts connus dans les théories de jauge N=1 sont reproduits, dont la condensation des gluinos et la brisure de la symétrie chirale.

Nous insistons sur les idées et les résultats plutôt que sur les détails techniques. Ceux-ci sont décrits dans la seconde partie de ce mémoire, qui consiste en une reproduction fidèle des travaux publiés durant cette thèse.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Eberle, Holger. « Conformal field theory between supersymmetry and indecomposable structures ». [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980709393.

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Franco, Sebastián Federico. « Duality and dynamics of supersymmetric field theories from D-branes on singularities ». Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32298.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
Includes bibliographical references (p. 359-373).
We carry out various investigations regarding gauge theories on the worldvolume of D-branes probing toric singularities. We first study the connection that arises in Toric Duality between different dual gauge theory phases and the multiplicity of fields in the gauged linear sigma models associated with the probed geometries. We introduce a straightforward procedure for the determination of toric dual theories and partial resolutions based on the (p, q) web description of toric singularities. We study the non-conformal theories that arise in the presence of fractional branes. We introduce a systematic procedure to study the resulting cascading RG flows, including the effect of anomalous dimensions on beta functions. Supergravity solutions dual to logarithmic RG flows are constructed, validating the field theory analysis of the cascades. We systematically study the IR dynamics of cascading gauge theories. We show how the deformation in the dual geometries is encoded in a quantum modification of the moduli space. We construct an infinite family of superconformal quiver gauge theories which are AdS/CFT dual to Sasaki-Einstein horizons with explicit metrics. The gauge theory and geometric computations of R-charges and central charges are shown to agree. We introduce new Type IIB brane constructions denoted brane tilings which are dual to D3-branes probing arbitrary toric singularities. Brane tilings encode both the quiver and superpotential of the gauge theories on the D-brane probes. They give a connection with the statistical model of dimers.
(cont.) They provide the simplest known method for computing toric moduli spaces of gauge theories, which reduces to finding the determinant of the Kasteleyn matrix of a bipartite graph.
by Sebastián Federico Franco.
Ph.D.

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Wittig, John Rudolph Jr. « New Results in 4D N=2 Superconformal Field Theories ». University of Cincinnati / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1240853782.

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Guo, Jirui. « Chiral Rings of Two-dimensional Field Theories with (0,2) Supersymmetry ». Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77530.

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This thesis is devoted to a thorough study of chiral rings in two-dimensional (0,2) theories. We first discuss properties of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories. As a special case, we study the quantum sheaf cohomology of Grassmannians as a deformation of the usual quantum cohomology. The deformation corresponds to a (0,2) deformation of the nonabelian gauged linear sigma model whose geometric phase is associated with the Grassmannian. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. Supersymmetric localization is also applicable in this case, which proves to be efficient in computing A/2 correlation functions. We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to the Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points. As another application, we extend previous works to construct (0,2) Toda-like mirrors to the sigma model engineering Grassmannians.
Ph. D.

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Galteland, Peder Notto. « Symmetry Breaking in ordinary and supersymmetric Models of Quantum Field Theory ». Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-16794.

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This thesis will consider two different theories, and apply variational techniquesto each, in order to investigate their true ground states and the possibility ofsymmetry breaking.A scalar field theory is modified by introducing a variational mass-parameter,which also serves as a regularization. The effective potential is calculated to twoloops, and a variational calculation is done to find the extrema of the potential.Secondly, the model of Wess and Zumino is modified by removing the re-strictions on the particle masses. The vacuum energy is then calculated to twoloops, and a variational calculation is performed with the renormalized massesas parameters, in order to determine the true ground state of the theory.It is discovered that the scalar field theory does not develop any symme-trybreaking groundstates, as was predicted by Coleman and Weinberg. Thenon-renormalization and vanishing vacuum energy of the Wess-Zumino model isverifed to two-loop order. Furthermore, it is discovered that the modified Wess-Zumino model has several groundstates which are more energetically favouredthan the supersymmetric state, in which supersymmetry is strongly broken.This may begin explain, if they exist, why we do not see any supersymmetricpartners in our accelerators.

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Morales, Herbert. « BOSONIZATION VS. SUPERSYMMETRY ». UKnowledge, 2006. http://uknowledge.uky.edu/gradschool_diss/429.

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We study the conjectured equivalence between the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under a naive application of the bosonization rules. We start with a review of the equivalence between sine-Gordon model and the massive Thirring model. We study the models by perturbation theory and then determine the equivalence. We find that the dependence of the identifications on the couplings can change according to the definition of the vector current. With the operator identifications of the special case corresponding to a free fermionic theory, known as the bosonization rules, we describe the equivalence between the massless Thirring model and the model of a compactified free boson field. For the massless Thirring model, or equivalently the O(2) Gross-Neveu model, we study the conservation laws for the vector current and the axial current by employing a generalized point-splitting method which allows a one-parameter family of definitions of the vector current. With this parameter, we can make contact with different approaches that can be found in the literature; these approaches differ mainly because of the specific definition of the current that was used. We also find the Sugawara form of the stress-energy tensor and its commutation relations. Further, we rewrite the identifications between sine-Gordon and Thirring models in our generalized framework. For the O(3) Gross-Neveu model, we extend our point-splitting method to determine the exact expression for the supercurrent. Using this current, we compute the superalgebra which determines three quantum components of the stress-energy tensor. With an Ansatz for the undetermined component, we find the trace anomaly and the first beta-function coefficient. The central charge which can be computed without using our point-splitting method is independent of the coupling constant, in fact, it is always zero. For the supersymmetric sine-Gordon model, we review its supersymmetry in the context of models derived from a scalar multiplet in two dimensions. We then obtain the central charge and discover an extra term that was missing in the original derivation. We also analyze how normal ordering modifies the central charge. Finally, we discuss the conjectured equivalence of the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under the naive application of the bosonization rules. Comparing our results of the central charges and the supercurrents for these models, we find that they disagree; consequently the models should be generically inequivalent. We also conclude that the naive application of the bosonization rules at the Lagrangian level does not always lead to an equivalent theory.

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Berg, Gustav Marcus. « Geometry, renormalization, and supersymmetry / ». Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008275.

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Bertoldi, Gaetano 1973. « Analysis of supersymmetric field theories via AdS/CFT, brane setups and matrix models ». Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29611.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2003.
Includes bibliographical references (p. 113-124).
N = 1 theories whose matrix model spectral curve develops Argyres-Douglas singularities are constructed. The large N expansion breaks down at the critical points with domain wall tensions scaling as a fractional power of N. However, there exist double scaling limits that are conjectured to define a four-dimensional non-critical string theory. The confinement-deconfinement phase transition in 3d = 1 U(N) Super Yang-Mills Chern-Simons theory is studied via its supergravity dual description. The would-be deconfined higher temperature phase is actually unstable. Therefore, it is not possible to conclude whether the transition takes place or not. The splitting of NS5-branes and D(p+2)-branes on orientifold Op-planes is analyzed. The rules governing this process are derived and checked in the case p = 4 by means of Seiberg-Witten curves.
by Gaetano Bertoldi.
Ph.D.

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Wells, Robert Edward. « Current-current correlators in NRQCD and supersymmetric field theory on the lattice ». Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610372.

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Bergner, Georg. « Symmetries and the methods of quantum field theory : supersymmetry on a space-time lattice ». lizenzfrei lizenzfrei, 2009. http://nbn-resolving.de/urn:nbn:de:gbv:27-20100114-114026-3.

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Ablikim, Medina. « Boundary sinh-Gordon model and its supersymmetric extension ». Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4853/.

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Three different aspects of the sinh-Gordon model are explored in this thesis. We begin, in chapter one, with a summary of the model and the necessary background. Chapter two studies the model with two boundary conditions. Two approaches are presented to investigate the reflection factors off the boundaries and the energy of the theory. In chapter three, perturbation theory is developed to study the theory with one general boundary condition. A contribution to the quantum reflection factor is obtained and compared with the result obtained for the special boundary condition. Chapters four and five investigate the supersymmetric extension of the model in the presence of a single boundary. Firstly, the classical limits of the supersymmetric reflection matrices are checked. The exact reflection factors are studied perturbatively up to the second order of the coupling constant. Secondly, the perturbation theory and the path integral formalism are employed in the supersymmetric model to study the quantum reflection factors. We conclude with a brief sixth chapter describing the outlook for further investigations.

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Yamada, Daisuke. « Phase structure of maximally supersymmetric Yang-Mills theory with R-symmetry chemical potentials / ». Thesis, Connect to this title online ; UW restricted, 2006. http://hdl.handle.net/1773/9807.

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Nolte, Detlef Reinhard. « Topics in high energy physics : from supersymmetric gauge field theories to rare B meson decays / ». Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC IP addresses, 2000. http://wwwlib.umi.com/cr/ucsd/fullcit?p9974117.

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Buchberger, Igor. « Strings, Gravitons, and Effective Field Theories ». Doctoral thesis, Karlstads universitet, Institutionen för ingenjörsvetenskap och fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-41912.

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This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes.
Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory. With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

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Siggia, Vincent R. « An Introduction to Supersymmetric Quantum Mechanics ». VCU Scholars Compass, 2019. https://scholarscompass.vcu.edu/etd/5884.

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In this thesis, the general framework of supersymmetric quantum mechanics and the path integral approach will be presented (as well as the worked out example of the supersymmetric harmonic oscillator). Then the theory will be specialized to the case of supersymmetric quantum mechanics on Riemannian manifolds, which will start from a supersymmetric Lagrangian for the general case and the special case for S2. Afterwards, there will be a discussion on the superfield formalism. Concluding this thesis will be the Hamiltonian formalism followed by the inclusion of deforma- tions by potentials.

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de, lechtenf@itp uni-hannover. « N=(2$|$2) Supersymmetric Toda Lattice Hierarchy in N=(2$|$2) Superspace ». J. Nonlinear Math. Phys. 8 (2001) 183-195, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi913.ps.

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Baguet, Arnaud. « Exceptional Field Theory and Supergravity ». Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEN022/document.

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Dans cette thèse, nous présentons des avancements récents en Théorie des Champs Doubles (TCD) et Théories des Champs Exceptionnels (TCE). Ces théories ont la particularité d’être des reformulations de supergravité dans lesquelles les symétries de dualité sont explicites avant toute réduction dimensionnelle. Ces reformulations se basent sur la définition d’un espace-temps étendu qui géométrise le groupe de T-dualité en TCD et les groupes exceptionnels de U-dualité en TCE. Tous les champs de cet espace sont soumis à une contrainte de section qui restreint leur dépendance en coordonnées. Il existe plusieurs solutions à la contrainte de section, qui correspondent donc à des théories différentes. Dans ce sens, le formalisme des théories des champs étendues amène à une unification de ces théories. De plus, grâce à un outil spécifique aux théories des champs étendues, l’ansatz de Scherk-Schwarz généralisé, il est possible de réécrire les ansatz compliqué de type Kaluza-Klein en supergravité sous une forme élégante et compacte: un produit matriciel en dimensions supérieures. Ici, nous présentons plusieurs exemples de l’efficacité de l’ansatz de Scherk-Schwarz généralisé. En particulier, nous prouvons deux conjectures concernant les troncations cohérentes: la réduction dite “de Pauli” de la corde bosonique ainsi que la supergravité de type IIB sur AdS5 x S5. La dernière application de cet ansatz concerne la théorie de type IIB généralisée, apparue récemment dans l’étude des système intégrables, et son plongement dans la TCE E6(6). Enfin, nous présentons la complétion supersymétrique de la TCE E8(8) bosonique
In this thesis, recent developments in Double Field Theory (DFT) and Exceptional Field Theory (EFT) are presented. They are reformulation of supergravity in which duality symmetries are made manifest before dimensional reduction. This is achieved through the definition of an extended spacetime that “geometrises” the T-duality group O(d,d) in DFT and exceptional U-duality groups in EFT. All functions on this extended space are subject to a covariant `section constraint', whose solutions then restrict the coordinates dependency of the fields. There exist different solutions to the section constraint that correspond to different theories. In this sense, different theories are unified within the formalism of extended field theories. Moreover, extended field theories possess a powerful tool to study compactifications: the generalised Scherk-Schwarz ansatz.Here, we present several examples of the effectiveness of the generalised Scherk-Schwarz ansatz. In particular, we proved two conjectures regarding consistent truncations: the so-called Pauli reduction of the bosonic string on group manifolds and type IIB supergravity on AdS5 x S5. Another application is presented on the embedding of generalised type IIB within the E6(6) EFT, which recently appeared in the study of integrable systems.Finally, we present the supersymmetric completion of the bosonic E8(8) EFT

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Vargas, Carlos Bercini. « Estudos sobre teorias quânticas de campos integráveis em duas dimensões ». Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-08102018-150801/.

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Esta dissertação de mestrado consiste de uma revisão sobre teorias quânticas de campos integráveis em duas dimensões, explorando tanto aspectos clássicos como aspectos quânticos dessas teorias munidas de infinitas cargas conservadas. Em nível clássico, consideramos uma teoria de supercampos escalares em duas dimensões com superpotencial arbitrário. Através da imposição da não produção de partículas a nível-árvore, restringimos a forma das interações adimissíveis, recuperando uma extensão supersimétrica do modelo de sinh-Gordon, o qual é provado ser integrável não somente através da obtenção do conjunto infinito de cargas conservadas, mas também através de S-matrix bootstrap. Ainda no nível clássico também mostramos uma profunda relação entre as Toda theories e os conformal minimal models, a qual se estende para nível quântico onde obtemos uma família de fluxos de renormalização entre os unitary conformal minimal models conhecida como staircase model.
This master thesis is an overview of integrability in two-dimensional field theories. We explore both classical and quantum aspects of these theories which are characterized by infinitely many conserved charges. At the classical level, we consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree-level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric extension of the sinh-Gordon model. This model is proven to be integrable not only by explicitly finding the infinite set of conserved charges but also via the S-matrix bootstrap. We also show a deep relation between Affine Toda theories and conformal minimal models, that extends to the quantum level, where we find a family of integrable renormalization group flows between the unitary conformal minimal models, known as the staircase model.

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Heilmann, Marianne [Verfasser], Andreas [Akademischer Betreuer] Wipf, Frank [Akademischer Betreuer] Saueressig et Hidenori [Akademischer Betreuer] Sonoda. « A renormalization group study of supersymmetric field theories / Marianne Heilmann. Gutachter : Andreas Wipf ; Frank Saueressig ; Hidenori Sonoda ». Jena : Thüringer Universitäts- und Landesbibliothek Jena, 2015. http://d-nb.info/1076038867/34.

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O'Bannon, Andrew Hill. « Holographic thermodynamics and transport of flavor fields / ». Thesis, Connect to this title online ; UW restricted, 2008. http://hdl.handle.net/1773/9785.

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Troost, Jan. « Strings, links between conformal field theory, gauge theory and gravity ». Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00410720.

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La théorie de cordes unifie de façon naturelle les théories de jauge, qui décrivent les interactions entre les particules élémentaires, avec une théorie quantique de la gravitation. Ces dernières années ont apporté de grands progrès dans la compréhension des états non-perturbatifs de la théorie, ses aspects holographiques, ainsi que la construction de modèles proches du Modèle Standard. Néanmoins, il reste des défis pour la théorie de cordes, qui incluent une définition non-perturbative, une meilleure compréhension de l'holographie, et le problème de la constante cosmologique. Ma recherche s'est concentrée sur des aspects formels des théories de gravitation quantique, qui incluent les trous noirs, la dépendance du temps, et l'holographie. Gr^ace à de nouveaux résultats dans le domaine de la théorie conforme avec spectre continu, mes collaborateurs et moi-m^eme avons avancé dans la compréhension de l'holographie dans des fonds avec dilaton linéaire, ainsi que dans le plongement de théories de jauge supersymétriques dans la théorie de cordes. En particulier, on a étudié des théories conformes supersymétriques avec spectre continu que l'on utilise pour construire des fonds de théories de cordes non-compacts et courbés. Les résultats obtenus nous ont permis de décrire des exemples explicites de symétrie miroir pour des fonds non-compacts. En introduisant des bords dans les théories conformes, on a analysé des états non-perturbatifs de la théorie de cordes, les D-branes. A basse énergie, les degrés de liberté sur les D-branes interagissent par des interactions de jauge. Avec ces outils, on a réussi à plonger une dualité infrarouge de théorie de jauge supersymétrique dans la théorie de cordes, et on a montré que la dualité correspond à une monodromie pour les états de bord dans l'espace de modules de la théorie conforme.

Dans cette thèse, on discute de nombreux autres liens entre la théorie conforme, la théorie de jauge et la gravitation. La plupart des contributions décrites étaient motivées par la théorie de cordes. Des exemples sont l'analyse d'états qui préservent la supersymétrie et leur lien avec les algèbres affines, la dépendance du temps et le dictionnaire holographique, l'analyse directe de la quantification de la gravité en présence d'un trou noir, la réalisation du scenario sans-bord pour la fonction d'onde de l'univers en théorie de cordes, une formule de Verlinde pour les théories conformes non-rationnelles et la construction de solutions non-géometriques à la supergravité. Dans d'autres travaux, je me suis concentré sur des théories qui quantifient la gravité plus directement, mais qui pourraient avoir moins de succès dans le problème de l'unification des forces en quatre dimensions. Ces théories ont quand-m^eme le potentiel de nous apprendre des aspects communs à toute théorie de gravitation quantique. Par exemple, on a analysé les degrés de liberté responsables de l'entropie d'un trou noir en trois dimensions, et nous avons argumenté sur la difficulté de reconcilier l'invariance modulaire avec l'unitarité en dehors de la théorie de cordes. On a aussi discuté la diffusion de ces trous noirs. D'autres contributions à la théorie de jauge non-commutative, la théorie de jauge supersymétrique, la production de paires dans un espace courbe, et cetera, sont aussi relativement indépendantes du cadre de la théorie de cordes.

Il me semble qu'il reste intéressant d'étudier des questions difficiles sur la théorie de jauge et la gravitation quantique, dans la cadre de la théorie de cordes, et en dehors de ce cadre, et d'^etre guidé par des problèmes ouverts durs qui doivent mener à un progrès concret par incréments ou par sauts.

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Clark, Adam Benjamin. « Applications of conformal perturbation theory to novel geometries in the gauge/gravity correspondence / ». Thesis, Connect to this title online ; UW restricted, 2006. http://hdl.handle.net/1773/9789.

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45

Synatschke-Czerwonka, Franziska [Verfasser], Andreas Akademischer Betreuer] Wipf, Martin [Akademischer Betreuer] [Reuter et Daniel [Akademischer Betreuer] Litim. « Functional Renormalisation Group Equitions for Supersymmetric Field Theories / Franziska Synatschke-Czerwonka. Gutachter : Andreas Wipf ; Martin Reuter ; Daniel Litim ». Jena : Thüringer Universitäts- und Landesbibliothek Jena, 2011. http://d-nb.info/1016619995/34.

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Pais, Hirigoyen Pablo. « Unconventional Supersymmetry, Massless Rarita-Schwinger Theory and Strained Graphene ». Doctoral thesis, Universite Libre de Bruxelles, 2017. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/258427.

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In this Thesis, we propose to analyze three different aspects of Fundamental Physics.The first part is devoted to the detailed study of what is called "unconventional supersymmetry" in three and four dimensions for Abelian and non-Abelian internal groups. We show the dynamical content of the odd-dimensional theory, counting at the same time the local degrees of freedom for some particular sectors of the phase space. In the non-Abelian three-dimensional case, some black hole solutions are presented, including their Killing spinors. In four dimensions, the supersymmetry is broken explicitly and a standard Dirac Lagrangian coupled with the electromagnetic field and the background geometry is obtained.In the second part, the dynamical content for the free and gauge coupled massless Rarita-Schwinger theory is presented. We are able to do that through the Dirac's Hamiltonian formalism and the Faddeev-Jackiw method, showing at the same time the symmetries of the theory. It is shown that in the gauge extended theory, which includes extra fermionic fields to restore the fermionic symmetries of the free case, the anticommutator of the Rarita-Schwinger field in the canonical quantization is not positive definite in general.As the graphene has been proposed as an on ``table-top laboratory" for some Quantum Gravity scenarios, in the third part of this Thesis we clarify some subtle features of strained graphene in order to manage properly this material. We show particularly that the pseudo-magnetic field induced by the in-plane strain tensor field cannot emerge from a Quantum Field Theory in curved spacetime approach (bottom-up approach) but from the detailed analysis of the tight-binding Hamiltonian of pi electrons in graphene (top-down approach) instead.
Dans cette Thèse, nous nous proposons d'analyser trois aspects différents de la Physique Fondamentale.La première partie est consacrée à l'éude détaillée de ce qu'on appelle "supersymétrie non conventionnelle" à trois et quatre dimensions pour des groupes internes abéliens et non abéliens. Nous montrons le contenu dynamique de la théorie de la dimension impaire, comptant en même temps les degrés de liberté locaux pour certains secteurs particuliers de l'espace des phases. Dans le cas tridimensionnel non-abélien, certaines solutions de trous noirs sont présentées, y compris leurs spinors de Killing. En quatre dimensions, la supersymétrie est brisée explicitement et un Lagrangien de Dirac standard couplé à l'électromagnétisme et à la géométrie d'arriére-plan est obtenu.Dans la deuxième partie, le contenu dynamique de la théorie de Rarita-Schwinger libre et couplée à un champ de jauge sans masse est présenté. Nous sommes en mesure de le faire par le formalisme Hamiltonien de Dirac et la méthode dite de Faddeev-Jackiw, en montrant en même temps les symétries de la théorie. Il est démontré que dans la théorie étendue de jauge, qui comprend des champs fermioniques supplémentaires pour restaurer les symétries fermioniques du cas libre, l'anticommutator du champ Rarita-Schwinger dans la quantification canonique n'est pas définiti positif en général.Comme le graphène a été proposé comme un "laboratoire de table" pour certains scénarios de gravité quantique, dans la troisième partie de cette Thèse, nous clarifions certaines caractéristiques subtiles du graphène sous tension afin de gérer correctement ce matériel. Nous montrons en particulier que le champ pseudo-magnétique induit par le champ tensoriel de déformation dans le plan ne peut pas émerger d'une théorie de champ quantique dans un espace courbe (approche bottom-up), mais bien à partir de l'analyse détaillée de l'Hamiltonien tight-binding des pi électrons dans le graphène (approche top-down).
En esta Tesis se propone analizar tres aspectos diferentes de la Física Fundamental.La primera parte está dedicada al estudio detallado de lo que ha pasado a llamarse "supersimetría no convencional" en tres y cuatro dimensiones para grupos internos abelianos y no abelianos. Se muestra el contenido dinámico en dimensiones impares de la teoría, contando al mismo tiempo los grados de libertad locales para ciertos sectores del espacio de fases. En el caso tridimensional no abeliano, se presentan algunas soluciones de agujeros negros, incluyendo sus espinores de Killing. En cuatro dimensiones, la supersimetría está rota explícitamente y se obtiene un lagrangiano estándar de Dirac acoplado con el campo electromagnético y la geometría de fondo.En la segunda parte, se presenta el contenido dinámico de la teoría de Rarita-Schwinger libre y con acoplamiento gauge. Esto se puede hacer a través del formalismo hamiltoniano de Dirac y el método de Faddeev-Jackiw, mostrando al mismo tiempo las simetrías de la teoría. Se observa que en la teoría gauge extendida, la cual incluye campos fermiónicos extra para restaurar la simetría fermiónica del caso libre, el anticonmutador del campo de Rarita-Schwinger no es definido positivo en la cuantización canónica.Ya que el grafeno se ha propuesto como una "mesa de laboratorio" para algunos escenarios de gravedad cuántica, en la tercera parte de esta Tesis se clarifican algunas características sutiles del grafeno extendido con el objetivo de manejar debidamente el material. Se muestra particularmente que el campo seudo-magnético inducido por el campo de tensión planar no puede emerger de una teoría cuántica de campos en espacios curvos (abordaje top-down), sino de un análisis detallado del hamiltoniano tight-binding de los electrones pi en el grafeno (abordaje bottom-up).
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Grasso, Darren Trevor. « Higher order contributions to the effective action of N = 2 and 4 supersymmetric Yang-Mills theories from heat kernel techniques in superspace ». University of Western Australia. School of Physics, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0179.

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The one-loop effective action for N = 2 and N = 4 supersymmetric Yang-Mills theories are computed to order F5; and F6 respectively by the use of heat kernel techniques in N = 1 superspace. The computations are carried out via the introduction of a new method for computing DeWitt-Seeley coefficients in the coincidence limit. To order F5, the bosonic components of both N = 2 and N = 4 supersymmetric Yang-Mills theories are extracted and compared with the existing literature. For N = 4 super Yang-Mills theories the F5 terms are found to be consistent with the non-Abelian Born-Infeld action computed to this order by superstring methods and various other means of computing deformations of supersymmetric Yang-Mills theory. The result proved to be the final piece of a puzzle, leaving little doubt that there exists a unique deformation of maximally symmetric super Yang-Mills theories at this order. The F6 terms will be of importance for comparison with superstring calculations, including direct tests of the AdS/CFT conjecture. The bosonic components of N = 2 supersymmetric Yang-Mills are also shown to be consistent with existing literature, and will be of importance for testing of generalizations of the AdS/CFT conjecture.

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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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Grozdanov, Saso. « Hydrodynamics : from effective field theory to holography ». Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:c00bd3e6-3b52-41d5-8542-2f2d55fc8741.

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Hydrodynamics is an effective theory that is extremely successful in describing a wide range of physical phenomena in liquids, gases and plasmas. However, our understanding of the structure of the theory, its microscopic origins and its behaviour at strong coupling is far from complete. To understand how an effective theory of dissipative hydrodynamics could emerge from a closed microscopic system, we analyse the structure of effective Schwinger-Keldysh Closed-Time-Path theories. We use this structure and the action principle for open systems to derive the energy-momentum balance equation for a dissipative fluid from an effective CTP Goldstone action. Near hydrodynamical equilibrium, we construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations. Shear viscosity is shown to vanish, while bulk viscosity and thermodynamical quantities are determined by the form of the effective action. The exploration of strongly interacting states of matter, particularly in the hydrodynamic regime, has been a major recent application of gauge/string duality. The strongly coupled theories involved are typically deformations of large-$N$ SUSY gauge theories with exotic matter that are unusual from a low-energy point of view. In order to better interpret holographic results, an understanding of the weak-coupling behaviour of such gauge theories is essential. We study the exact and SUSY-broken N=1 and N=2 super-QED with finite densities of electron number and R-charge, respectively. Despite the fact that fermionic fields couple to the chemical potentials, the strength of scalar-fermion interactions, fixed by SUSY, prevents a Fermi surface from forming. This is important for hydrodynamical excitations such as zero sound. Intriguingly, in the absence of a Fermi surface, the total charge need not be stored in the scalar condensates alone and fermions may contribute. Gauss-Bonnet gravity is a useful laboratory for non-perturbative studies of the higher derivative curvature effects on transport coefficients of conformal fluids with holographic duals. It was previously known that shear viscosity can be tuned to zero by adjusting the Gauss-Bonnet coupling, λ_GB, to its maximal critical value. To understand the behaviour of the fluid in this limit, we compute the second-order transport coefficients non-perturbatively in λ_GB and show that the fluid still produces entropy, while diffusion and sound attenuation are suppressed at all order in the hydrodynamic expansion. We also show that the theory violates a previously proposed universal relation between three of the second order transport coefficients. We further compute the only second-order coefficient thus far unknown, λ₂, in the N=4 super Yang-Mills theory with the leading-order 't Hooft coupling correction. Intriguingly, the universal relation is not violated by these leading-order perturbative corrections. Finally, by adding higher-derivative photon field terms to the action, we study charge diffusion and non-perturbative parameter regimes in which the charge diffusion constant vanishes.

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ROSA, DARIO. « From spinors to forms : results on g-structures in supergravity and on topological field theories ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/55207.

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This thesis is divided in two parts, that can be read separately even if both use the possibility of replacing spinors with differential forms in theories with supersymmetry. The ﬁrst part explores some recent results that have been obtained by applying the G-structure approach to type II supergravities. Using generalized complex geometry it is possible to reformulate the conditions for unbroken supersymmetry in type II supergravity in terms of differential forms. We use this result to ﬁnd a classiﬁcation for AdS7 and AdS6 solutions in type II supergravity. Concerning AdS7 solutions we ﬁnd that in type IIB no solutions can be found, whereas in massive type IIA many new AdS7×M3 solutions are at disposal with the topology of the internal manifold M3 given by a three-sphere. We develop a classiﬁcation for such solutions. Concerning AdS6 solutions, very few AdS6×M4 supersymmetric solutions are known in literature: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique. We obtain a classiﬁcation for IIB supergravity, by reducing the problem to two PDEs on a two-dimensional space Σ. The four-dimensional space M4 is then given by a ﬁbration of S2 over Σ. We also explore other two contexts in which the G-structure approach has revealed its usefulness: ﬁrst of all we derive the conditions for unbroken supersymmetry for a Mink2 (2,0) vacuum, arising from type II supergravity on a compact eight-dimensional manifold M8. When M8 enjoys SU(4)×SU(4) structure the resulting system is elegantly rewritten in terms of generalized complex geometry. Finally we rewrite the equations for ten-dimensional supersymmetry in a way formally identical to an analogous system in N = 2 gauged supergravity; this provides a way to look for lifts of BPS solutions without having to reduce the ten-dimensional action. The second part is devoted to study some aspects of two different Chern-Simons like theories: holomorphic Chern-Simons theory on a six-dimensional Calabi-Yau space and three-dimensional supersymmetric theories involving vector multiplets (both with Yang-Mills and Chern-Simons terms in the action). Concerning holomorphic Chern-Simons theory, we construct an action that couples the gauge ﬁeld to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of this off-shell action is achieved by enlarging the ﬁeld space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost ﬁelds. From this reformulation it is possible to uncover a twisted supersymmetric algebra for this model that strongly constrains the anti-holomorphic dependence of physical correlators. Concerning three-dimensional theories, we will develop a new way of computing the exact partition function of supersymmetric three-dimensional gauge theories, involving vector supermultiplet only. Our approach will reduce the problem of computing the exact partition function to the problem of solving an anomalous Ward identity. To obtain such a result we will describe the coupling of three-dimensional topological gauge theories to background topological gravity. The Seifert condition for manifolds supporting global supersymmetry is elegantly deduced from the topological gravity BRST transformations. We will show how the geometrical moduli that affect the partition function can be characterized cohomologically. In the Seifert context Chern-Simons topological (framing) anomaly is BRST trivial and we will compute explicitly the corresponding local Wess-Zumino functional. As an application, we obtain the dependence on the Seifert moduli of the partition function of three-dimensional supersymmetric gauge theory on the squashed sphere by solving the anomalous topological Ward identities, in a regularization independent way and without the need of evaluating any functional determinant.

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Thèses sur le sujet « Supersymmetric field theorie »

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