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Dissertations / Theses on the topic 'Topological strings'

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Published: 14 March 2023

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1

Goodband, Michael James. "Perturbations about topological defects." Thesis, University of Sussex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336276.

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2

Hecht, Michael. "Effective actions and topological strings." Diss., lmu, 2011. http://nbn-resolving.de/urn:nbn:de:bvb:19-135759.

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3

Gu, Jie [Verfasser]. "Braiding Knots with Topological Strings / Jie Gu." Bonn : Universitäts- und Landesbibliothek Bonn, 2015. http://d-nb.info/1079273425/34.

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4

Chuang, Wu-yen. "Geometric transitions, topological strings, and generalized complex geometry /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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5

Gill, Alasdair James. "Field theory and topological defects." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244675.

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6

Martin, Adrian Peter. "Cosmological phase transition phenomena." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389880.

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7

Hecht, Michael [Verfasser], and Peter [Akademischer Betreuer] Mayr. "Effective actions and topological strings : Off-shell mirror symmetry and mock modularity of multiple M5-branes / Michael Hecht. Betreuer: Peter Mayr." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2011. http://d-nb.info/1016615329/34.

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8

Melo, dos Santos Luis F. "Aspects of topological string theory." Thesis, Imperial College London, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.516484.

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9

Duan, Zhihao. "Topological string theory and applications." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE011/document.

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Cette thèse porte sur diverses applications de la théorie des cordes topologiques basée sur différents types de variétés de Calabi-Yau (CY). Le premier type considéré est la variété torique CY, qui est intimement liée aux problèmes spectraux des différents opérateurs. L'exemple particulier considéré dans la thèse ressemble beaucoup au modèle de Harper-Hofstadter en physique de la matière condensée. Nous étudions d’abord les secteurs non perturbatifs dans ce modèle et proposons une nouvelle façon de les calculer en utilisant la théorie topologique des cordes. Dans la deuxième partie de la thèse, nous considérons les fonctions de partition sur des variétés de CY elliptiquement fibrées. Celles-ci présentent un comportement modulaire intéressant. Nous montrons que pour les géométries qui ne conduisent pas à des symétries de jauge non abéliennes, les fonctions de partition des cordes topologiques peuvent être reconstruites avec seulement les invariants de Gromov-Witten du genre zéro. Finalement, nous discutons des travaux en cours concernant la relation entre les fonctions de partitionnement des cordes topologiques sur les soi-disant arbres de Higgsing dans la théorie de F
This thesis focuses on various applications of topological string theory based on different types of Calabi-Yau (CY) manifolds. The first type considered is the toric CY manifold, which is intimately related to spectral problems of difference operators. The particular example considered in the thesis closely resembles the Harper-Hofstadter model in condensed matter physics. We first study the non-perturbative sectors in this model, and then propose a new way to compute them using topological string theory. In the second part of the thesis, we consider partition functions on elliptically fibered CY manifolds. These exhibit interesting modular behavior. We show that for geometries which don't lead to non-abelian gauge symmetries, the topological string partition functions can be reconstructed based solely on genus zero Gromov-Witten invariants. Finally, we discuss ongoing work regarding the relation of the topological string partition functions on the so-called Higgsing trees in F-theory
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10

Gregory, Ruth Ann Watson. "Topological defects in cosmology." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292897.

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11

Cooper, Leith. "The topological membrane approach to string theory." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390412.

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12

Dando, Owen Robert. "Topological defects in low-energy string gravity." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4496/.

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Cosmologists are interested in topological defects as a possible source for the primordial density perturbations which seeded structure formation through gravitational instability. In this thesis, the gravitational properties of various topological defects are studied in the context of low-energy string theory, a likely modification of Einstein gravity at the high energy scales prevalent in the early universe. We consider in turn global monopole, local monopole, global cosmic string and global texture defects, allowing for an arbitrary coupling of defects to the string theory dilaton. For global defects we find the following behaviour. If the dilaton is massless, this modification to general relativity generically destroys the global good behaviour of the monopole and cosmic string, making their spacetimes singular. For the texture non-singular spacetimes exist, but only for certain values of the matter-dilaton coupling, dependent on the gravitational strength of the defect; in addition, this non-singular behaviour exists only in a certain frame. In the case of a massive dilaton, the metric behaviour of these defects is similar to that found in Einstein gravity, though we find they generically induce a long-range dilaton cloud. For the local monopole, which we study only in the presence of a massless dilaton, a rich variety of behaviour is found. For particular parameter values the local monopole spacetime approximates that of an extremal dilaton black hole.
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13

Zein, Assi Ahmad. "Topological Amplitudes and the String Effective Action." Palaiseau, Ecole polytechnique, 2013. https://theses.hal.science/docs/00/94/40/86/PDF/TheseZeinAssiFinalv2.pdf.

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Cette thèse est dédiée à l'étude d'une classe de couplages dans l'action effective de la théorie des cordes qui se trouvent au croisement entre la théorie des cordes topologique et les théories de jauge supersymétriques. Ces couplages généralisent un ensemble de couplages gravitationnels qui calculent la fonction de partition de la théorie des cordes topologique. Dans la limite de théorie des champs, ces derniers reproduisent la fonction de partition de la théorie de jauge dans le fond Oméga lorsque l'un des paramètres de ce dernier, epsilon_+ , est égal à zéro. Cela suggère naturellement l'existence d'une généralisation dénommée la corde topologique raffinée. Les couplages étudiés dans ce manuscrit sont caractérisés par un multiplet vectoriel supplémentaire et sont calculés, en théorie des cordes, aux niveaux perturbatif et non-perturbatif. De plus, leur limite de théorie des champs donne la fonction de partition de la théorie des champs dans un fond Oméga général. Ainsi, ces couplages ouvrent de nouvelles perspectives pour la définition, au niveau de la surface d'univers, de la théorie des cordes topologiques raffinée
In this thesis, we study a class of higher derivative couplings in the string effective action arising at the junction of topological string theory and supersymmetric gauge theories in the Omega-background. They generalise a series of gravitational couplings involving gravitons and graviphotons, which reproduces the topological string theory partition function. The latter reduces, in the field theory limit, to the partition function of the gauge theory in the Omega-background when one if its parameters, say epsilon_+, is set to zero. This suggests the existence of a one-parameter extension called the refined topological string. The couplings considered in this work involve an additional vector multiplet and are evaluated, perturbatively and non-perturbatively, at the string level. In the field theory limit, they correctly reproduce the partition function of the gauge theory in a general Omega-background. Hence, these couplings provide new perspectives toward a worldsheet definition of the refined topological string
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14

Okuda, Takuya Ooguri Hirosi. "Large N dualities in topological string theory /." Diss., Pasadena, Calif. : California Institute of Technology, 2005. http://resolver.caltech.edu/CaltechETD:etd-05232005-184326.

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15

Krefl, Daniel. "Real Mirror Symmetry and The Real Topological String." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-102832.

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16

Kay, Michael. "On deformations and quantization in topological string theory." Diss., Ludwig-Maximilians-Universität München, 2014. http://nbn-resolving.de/urn:nbn:de:bvb:19-170482.

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Die Untersuchung der Moduli Räumen von N = (2,2) Superkonformen Feldtheorien und der allgemeineren N = (2,2) Supersymmetrischen Quanten Feldtheorien ist ein langjähriges und vielseitiges Forschungsgebiet. Diese Dissertation konzentriert sich auf gewisse allgemeine Aspekte des erwähnten Studiums, und stellt Entwicklungen von allgemeinen Methoden im Rahmen der Topologischen String Theorie dar. Die vorliegende Arbeit besteht aus zwei Teilen. Der erste Teil befasst sich mit Aspekten der geschlossenen Topologischen String Theorie und kulminiert in den Inhalt von [52], wo die geometrische Struktur der Topologischen anti-Topologischen Moduli Räumen von N = (2, 2) Superkonformen Feldtheorien mit Zentral Ladung c = 9, angesichts eines allgemeinen Quantisieung-Rahmens [31, 32] wiederentdeckt wird. Aus dieser Sichtweise erhält man, als Spezialfall, eine klare Einsicht der “holomorphic anomaly equation” von [6]. Diese Arbeit könnte als eine natürliche Erweiterung von früheren Untersuchungen in ähnlicher Richtung betrachtet werden, insbesondere vom grundlegenden Artikel [104]. Der zweite Teil befasst sich mit Aspekten der Untersuchung der Offenen und Geschlossenen Moduli Räumen von Topologischen Konformen Feldtheorien auf Genus Null. Insbesondere, ist hier eine Exposition von [13] enthalten, wo allgemeine Resultate über die Klassifizierung und Berechnung von “bulk-induced” Deformationen von Offenen Topologischen Konformen Feldtheorien erhalten wurden. Letzteres wurde durch eine kohärente algebraische Methode erreicht was sich auf den definierenden L∞ und A∞ beteiligten Strukturen bezieht. Teilweise ist die letztere Untersuchung auf beliebige Affine B-twisted Landau Ginzburg Modelle beschränkt. Nachfolgend wird weitere originelle Arbeit dargestellt was die Topologische String-Feld-Theoretische Struktur von B-twisted Landau Ginzburg Modellen vollendet. Insbesondere wird eine “off-shell” Erweiterung der Kapustin-Li Formel von [41, 49] gegeben. Diese “off-shell” Formel bezeichnet einen konsolidierenden Baustein der algebraischen Herangehensweise zur Berechnung des Effektiven Superpotentials von B-twisted Affine Landau Ginzburg Modellen, und kann damit als eine natürliche Entwicklung von der grundlegenden Arbeit [12] betrachtet werden.
The study of moduli spaces of N = (2, 2) superconformal field theories and more generally of N = (2, 2) supersymmetric quantum field theories, has been a longstanding, multifaceted area of research. In this thesis we focus on certain selected general aspects of this study and develop general techniques within the framework of topological string theory. This work is naturally divided into two parts. The first is concerned with aspects of closed topological string theory, and culminates with the content of [52], where the geometrical structure of the topological anti-topological moduli spaces of N = (2,2) superconformal field theories with central charge c = 9 is rediscovered in the light of quantization, within a general framework ([31, 32]). From this point of view, one thus obtains, as a special case, a clear understanding of the holomorphic anomaly equation of [6]. This work can be viewed as a natural continuation of earlier studies in the same direction, most notably the seminal paper [104]. The second part is concerned with aspects of the study of the open and closed moduli space of topological conformal field theories at genus zero. In particular, it contains an exposition of [13], where general results on the classification and computation of bulk- induced deformations of open topological conformal field theories were obtained from a coherent algebraic approach, drawing from the defining L∞ and A∞ structures involved. In part, the latter investigation is restricted to arbitrary affine B-twisted Landau Ginzburg models. Subsequently, further original work is presented that completes the topological string field theory structure of B-twisted Landau Ginzburg models, providing in particular an off-shell extension of the Kapustin-Li pairing of [41, 49]. This off-shell pairing constitutes a consolidating building block in the algebraic approach to the computation of the effective superpotential of B-twisted affine Landau Ginzburg models pioneered in [12].
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17

Ferreira, Pedro Castelo-Caetano. "Heterotic, open and unoriented string theories from topological membrane." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393440.

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18

Vincent, Graham Richard. "The evolution of gauged cosmic string networks." Thesis, University of Sussex, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390521.

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19

Alim, Murad. "Mirror Symmetry, Toric Branes and Topological String Amplitudes as Polynomials." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-103416.

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20

Rauch, Marco [Verfasser]. "Topological string theory, modularity and non-perturbative physics / Marco Rauch." Bonn : Universitäts- und Landesbibliothek Bonn, 2011. http://d-nb.info/1016219601/34.

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21

Levin, Michael Aaron Ph D. Massachusetts Institute of Technology. "String-net condensation and topological phases in quantum spin systems." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/36810.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
Includes bibliographical references (p. 81-86).
For many years, it was thought that Landau's theory of symmetry breaking could describe essentially all phases and phase transitions. However, in the last twenty years, it has become clear that at zero temperature, quantum mechanics allows for the possibility of new phases of matter beyond the Landau paradigm. In this thesis, we develop a general theoretical framework for these "exotic phases" analogous to Landau's framework for symmetry breaking phases. We focus on a particular type of exotic phase, known as "topological phases", and a particular physical realization of topological phases - namely frustrated quantum magnets. Our approach is based on a new physical picture for topological phases. We argue that, just as symmetry breaking phases originate from the condensation of particles, topological phases originate from the condensation of extended objects called "string-nets." Using this picture we show that, just as symmetry breaking phases can be classified using symmetry groups, topological phases can be classified using objects known as "tensor categories."
(cont.) In addition, just as symmetry breaking order manifests itself in local correlations in a ground state wave function, topological order manifests itself in nonlocal correlations or quantum entanglement. We introduce a new quantity - called "topological entropy" - which measures precisely this nonlocal entanglement. Many of our results are applicable to other (non-topological) exotic phases.
by Michael Aaron Levin.
Ph.D.
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22

Kay, Michael [Verfasser], and Ilka [Akademischer Betreuer] Brunner. "On deformations and quantization in topological string theory / Michael Kay. Betreuer: Ilka Brunner." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2014. http://d-nb.info/1052779190/34.

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23

Zhou, Jie. "Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11352.

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This thesis studies certain aspects of the global properties, including geometric and arithmetic, of the moduli spaces of complex structures of some special Calabi-Yau threefolds (B-model), and of the corresponding topological string partition functions defined from them which are closely related to the generating functions of Gromov-Witten invariants of their mirror Calabi-Yau threefolds (A-model) by the mirror symmetry conjecture.
Mathematics
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24

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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25

Cândido, Diogo Brum. "Controle supervisório aplicado a sistemas fotovoltaicos autônomos com topologia multi string." Universidade Federal de Santa Maria, 2010. http://repositorio.ufsm.br/handle/1/8479.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico
This master thesis analyses and implements a stand-alone photovoltaic system based on decentralized Multi String topology. The proposed system is composed of a set of DCDC converters linked to the PV arrays of panels, a bidirectional converter to perform the control of the charge/discharge process of the battery bank and ensure the specifications of DC link and a full-bridge inverter that feed the AC loads. Therefore, all operation modes that the stand-alone PV system can work are presented and analyzed. As the chief aim is to ensure the energy balance of the stand-alone PV system, are presented independents control loops for each converter of the PV system and a propose of a supervisory control that, based on information about the conditions of the DC link and the bank of batteries, defines each operation mode should be active, in order to maximize the power extracted from the PV arrays, the life cycle of the battery bank and ensuring the uninterrupted feeding of energy to the loads. Finally, simulation and experimental results validate the operation of the proposed system under different load and solar radiation conditions.
Este trabalho analisa e implementa um sistema fotovoltaico autônomo baseado no conceito de topologia descentralizada do tipo Multi String . O sistema proposto é constituído de um conjunto de conversores CC-CC vinculados aos arranjos de painéis, um conversor bidirecional para controle da carga e descarga do banco de baterias e um inversor de saída que fornece a alimentação CA as cargas. Todos os modos de operação em que o sistema PV autônomo proposto pode funcionar são apresentados e analisados. Com o objetivo principal de assegurar o balanço de energia do sistema PV autônomo, são apresentadas malhas de controle independentes para cada conversor do sistema PV e a proposta de um sistema supervisório o qual, de posse de informações sobre o estado do barramento CC e banco de baterias, define qual modo de operação deve estar ativo, maximizando a potência extraída dos arranjos PV, a vida útil do banco de baterias e garantindo um fornecimento contínuo de energia às cargas. Por fim, resultados de simulação e experimentais validam o funcionamento do sistema proposto em diferentes condições de carga e radiação solar.
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26

Källén, Johan. "Twisting and Gluing : On Topological Field Theories, Sigma Models and Vertex Algebras." Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-173225.

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This thesis consists of two parts, which can be read separately. In the first part we study aspects of topological field theories. We show how to topologically twist three-dimensional N=2 supersymmetric Chern-Simons theory using a contact structure on the underlying manifold. This gives us a formulation of Chern-Simons theory together with a set of auxiliary fields and an odd symmetry. For Seifert manifolds, we show how to use this odd symmetry to localize the path integral of Chern-Simons theory. The formulation of three-dimensional Chern-Simons theory using a contact structure admits natural generalizations to higher dimensions. We introduce and study these theories. The focus is on the five-dimensional theory, which can be understood as a topologically twisted version of N=1 supersymmetric Yang-Mills theory. When formulated on contact manifolds that are circle fibrations over a symplectic manifold, it localizes to contact instantons. For the theory on the five-sphere, we show that the perturbative part of the partition function is given by a matrix model. In the second part of the thesis, we study supersymmetric sigma models in the Hamiltonian formalism, both in a classical and in a quantum mechanical setup. We argue that the so called Chiral de Rham complex, which is a sheaf of vertex algebras, is a natural framework to understand quantum aspects of supersymmetric sigma models in the Hamiltonian formalism. We show how a class of currents which generate symmetry algebras for the classical sigma model can be defined within the Chiral de Rham complex framework, and for a six-dimensional Calabi-Yau manifold we calculate the equal-time commutators between the currents and show that they generate the Odake algebra.
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27

Schimannek, Thorsten [Verfasser]. "Aspects of Fibers, Fibrations and their Non-Compact Limits in F-theory and Topological String Theory / Thorsten Schimannek." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1167857100/34.

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28

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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29

Olsson, Martin. "String Theory at the Horizon : Quantum Aspects of Black Holes and Cosmology." Doctoral thesis, Uppsala University, Department of Theoretical Physics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5926.

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String theory is a unified framework for general relativity and quantum mechanics, thus being a theory of quantum gravity. In this thesis we discuss various aspects of quantum gravity for particular systems, having in common the existence of horizons. The main motivation is that one major challenge in theoretical physics today is in trying to understanding how time dependent backgrounds, with its resulting horizons and space-like singularities, should be described in a controlled way. One such system of particular importance is our own universe.

We begin by discussing the information puzzle in de Sitter space and consequences thereof. A typical time-scale is encountered, which we interpreted as setting the thermalization time for the system. Then the question of closed time-like curves is discussed in the combined setting where we have a rotating black hole in a Gödel-like universe. This gives a unified picture of what previously was considered as independent systems. The last three projects concerns $c=1$ matrix models and their applications. First in relation to the RR-charged two dimensional type 0A black hole. We calculate the ground state energy on both sides of the duality and find a perfect agreement. Finally, we relate the 0A model at self-dual radius to the topological string on the conifold. We find that an intriguing factorization of the theory previously observed for the topological string is also present in the 0A matrix model.

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30

Bonjour, Filipe. "Extended defects in curved spacetimes." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4966/.

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This Thesis is concerned with three particular aspects of extended cosmic strings and domain walls in cosmology: their dynamics, gravitation and interaction with a black hole. In Chapter 3, we study the dynamics of an abelian-Higgs cosmic string. We find its equations of motion from an effective action and compare, for three test trajectories, the resulting motion with that observed in the Nambu-Gotō approximation. We also present a general argument showing that the corrected motion of any string is generically antirigid. We pursue the investigation of the dynamics of topological defects in Chapter 5, where we find (from integrability conditions rather than an effective action) the effective equations governing the motion of a gravitating curved domain wall. In Chapter 4 we investigate the spacetime of a gravitating domain wall in a theory with a general potential V(ɸ). We show that, depending on the gravitational coupling e of the scalar ɸ, all nontrivial solutions fall into two categories interpretable as describing respectively domain wall and false vacuum-de Sitter solutions. Wall solutions cannot exist beyond a value (^4)(_3)ɛmax, and vacuum-de Sitter solutions are unstable to decaying into wall solutions below ɛmax at ɛmax we observe a phase transition between the two types of solution. We finally specialize for the Goldstone and sine-Gordon potentials. In Chapter 6 we consider a Nielsen-Olesen vortex whose axis passes through the centre of an extremal Reissner-Nordstr0m black hole. We examine in particular the existence of piercing and expelled solutions (where the string respectively does and does not penetrate the black hole's horizon) and determine that while thin strings penetrate the horizon — and therefore can be genuinely called hair — thick strings are expelled; the two kinds of solution are separated by a phase transition.
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31

Borot, Gaëtan. "Quelques problèmes de géométrie énumérative, de matrices aléatoires, d'intégrabilité, étudiés via la géométrie des surfaces de Riemann." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112092/document.

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La géométrie complexe est un outil puissant pour étudier les systèmes intégrables classiques, la physique statistique sur réseau aléatoire, les problèmes de matrices aléatoires, la théorie topologique des cordes, …Tous ces problèmes ont en commun la présence de relations, appelées équations de boucle ou contraintes de Virasoro. Dans le cas le plus simple, leur solution complète a été trouvée récemment, et se formule naturellement en termes de géométrie différentielle sur une surface de Riemann : la "courbe spectrale", qui dépend du problème. Cette thèse est une contribution au développement de ces techniques et de leurs applications.Pour commencer, nous abordons les questions de développement asymptotique à tous les ordres lorsque N tend vers l’infini, des intégrales N-dimensionnelles venant de la théorie des matrices aléatoires de taille N par N, ou plus généralement des gaz de Coulomb. Nous expliquons comment établir, dans les modèles de matrice beta et dans un régime à une coupure, le développement asymptotique à tous les ordres en puissances de N. Nous appliquons ces résultats à l'étude des grandes déviations du maximum des valeurs propres dans les modèles beta, et en déduisons de façon heuristique des informations sur l'asymptotique à tous les ordres de la loi de Tracy-Widom beta, pour tout beta positif. Ensuite, nous examinons le lien entre intégrabilité et équations de boucle. En corolaire, nous pouvons démontrer l'heuristique précédente concernant l'asymptotique de la loi de Tracy-Widom pour les matrices hermitiennes.Nous terminons avec la résolution de problèmes combinatoires en toute topologie. En théorie topologique des cordes, une conjecture de Bouchard, Klemm, Mariño et Pasquetti affirme que des séries génératrices bien choisies d'invariants de Gromov-Witten dans les espaces de Calabi-Yau toriques, sont solution d'équations de boucle. Nous l'avons démontré dans le cas le plus simple, où ces invariants coïncident avec les nombres de Hurwitz simples. Nous expliquons les progrès récents vers la conjecture générale, en relation avec nos travaux. En physique statistique sur réseau aléatoire, nous avons résolu le modèle O(n) trivalent sur réseau aléatoire introduit par Kostov, et expliquons la démarche à suivre pour résoudre des modèles plus généraux.Tous ces travaux soulignent l'importance de certaines "intégrales de matrices généralisées" pour les applications futures. Nous indiquons quelques éléments appelant à une théorie générale, encore basée sur des "équations de boucles", pour les calculer
Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory, … All these topics share certain relations, called "loop equations" or "Virasoro constraints". In the simplest case, the complete solution of those equations was found recently : it can be expressed in the framework of differential geometry over a certain Riemann surface which depends on the problem : the "spectral curve". This thesis is a contribution to the development of these techniques, and to their applications.First, we consider all order large N asymptotics in some N-dimensional integrals coming from random matrix theory, or more generally from "log gases" problems. We shall explain how to use loop equations to establish those asymptotics in beta matrix models within a one cut regime. This can be applied in the study of large fluctuations of the maximum eigenvalue in beta matrix models, and lead us to heuristic predictions about the asymptotics of Tracy-Widom beta law to all order, and for all positive beta. Second, we study the interplay between integrability and loop equations. As a corollary, we are able to prove the previous prediction about the asymptotics to all order of Tracy-Widom law for hermitian matrices.We move on with the solution of some combinatorial problems in all topologies. In topological string theory, a conjecture from Bouchard, Klemm, Mariño and Pasquetti states that certain generating series of Gromov-Witten invariants in toric Calabi-Yau threefolds, are solutions of loop equations. We have proved this conjecture in the simplest case, where those invariants coincide with the "simple Hurwitz numbers". We also explain recent progress towards the general conjecture, in relation with our work. In statistical physics on the random lattice, we have solved the trivalent O(n) model introduced by Kostov, and we explain the method to solve more general statistical models.Throughout the thesis, the computation of some "generalized matrices integrals" appears to be increasingly important for future applications, and this appeals for a general theory of loop equations
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32

"Phenomenology of Topological Solitons." Doctoral diss., 2020. http://hdl.handle.net/2286/R.I.57100.

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abstract: In this dissertation, I present the results from my recent investigations into the interactions involving topological defects, such as magnetic monopoles and strings, that may have been produced in the early universe. I performed numerical studies on the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. Sphaleron solution predicted by Taubes was recovered, and I mapped out its energy and size as functions of parameters. I also looked into the production, and decay modes of $U(1)$ gauge and global strings. I demonstrated that strings can be produced upon evolution of gauge wavepackets defined within a certain region of parameter space. The numerical exploration of the decay modes of cosmic string loops led to the conclusions that string loops emit particle radiation primarily due to kink collisions, and that their decay time due to these losses is proportional to $L^p$, where $L$ is the loop length and $p \approx 2$. In contrast, the decay time due to gravitational radiation scales in proportion to $L$, and I concluded that particle emission is the primary energy loss mechanism for loops smaller than a critical length scale, while gravitational losses dominate for larger loops. In addition, I analyzed the decay of cosmic global string loops due to radiation of Goldstone bosons and massive scalar ($\chi$) particles. The length of loops I studied ranges from 200-1000 times the width of the string core. I found that the lifetime of a loop is approximately $1.4L$. The energy spectrum of Goldstone boson radiation has a $k^{-1}$ fall off, where $k$ is the wavenumber, and a sharp peak at $k\approx m_\chi/2$, where $m_\chi$ is the mass of $\chi$. The latter is a new feature and implies a peak at high energies (MeV-GeV) in the cosmological distribution of QCD axions.
Dissertation/Thesis
Doctoral Dissertation Physics 2020
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33

Elliot, Ross Filip. "Topological Strings, Double Affine Hecke Algebras, and Exceptional Knot Homology." Thesis, 2015. https://thesis.library.caltech.edu/8920/1/Thesis.pdf.

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In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

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34

Cook, Paul Langabi Hogan. "Aspects of Topological String Theory." Thesis, 2008. https://thesis.library.caltech.edu/2174/1/thesis.pdf.

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Two aspects of the topological string and its applications are considered in this thesis. Firstly, non-perturbative contributions to the OSV conjecture relating four-dimensional extremal black holes and the closed topological string partition function are studied. A new technique is formulated for encapsulating these contributions for the case of a Calabi-Yau manifold constructed by fibering two line bundle over a torus, with the unexpected property that the resulting non-perturbative completion of the topological string partition function is such that the black hole partition function is equal to a product of a chiral and an anti-chiral function. This new approach is considered both in the context of the requirement of background independence for the topological string, and for more general Calabi-Yau manifolds. Secondly, this thesis provides a microscopic derivation of the open topological string holomorphic anomaly equations proposed by Walcher in arXiv:0705.4098 under the assumption that open string moduli do not contribute. In doing so, however, new anomalies are found for compact Calabi-Yau manifolds when the disk one-point functions (string to boundary amplitudes) are non-zero. These new anomalies introduce coupling to wrong moduli (complex structure moduli in A-model and Kahler moduli in B-model), and spoil the recursive structure of the holomorphic anomaly equations. For vanishing disk one-point functions, the open string holomorphic anomaly equations can be integrated to solve for amplitudes recursively, using a Feynman diagram approach, for which a proof is presented.
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35

Okuda, Takuya. "Large N Dualities in Topological String Theory." Thesis, 2005. https://thesis.library.caltech.edu/1977/1/thesis.pdf.

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We investigate the phenomenon of large N duality in topological string theory from three different perspectives: worldsheets, matrix models, and melting crystals.

In the first part, we utilize the technique of mirror symmetry to generalize the worldsheet derivation of the duality, originally given by Ooguri and Vafa for the A-model on the conifold, to the A-model on more general geometries. We also explain how the Landau-Ginzburg models can be used to perform the worldsheet derivation of the B-model large N dualities.

In the second part, we consider a class of A-model large N dualities where the open string theory reduces through the Chern-Simons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the Calabi-Yau geometry mirror to the closed string geometry, confirming the predictions of the duality.

Finally in the third part, we propose a crystal model that describes the A-model on the resolved conifold. This is a generalization of the crystal for C³. We also consider a novel unitary matrix model for the Chern-Simons theory on the three-sphere and show how the crystal model for the resolved conifold is derived from the matrix model. Certain non-compact D-branes are naturally incorporated into the crystal and the matrix model.

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36

Yang, Jie. "Holomorphic Anomaly Equations in Topological String Theory." Thesis, 2008. https://thesis.library.caltech.edu/2315/1/main.pdf.

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In this thesis we discuss various aspects of topological string theories. In particular we provide a derivation of the holomorphic anomaly equation for open strings and study aspects of the Ooguri, Strominger, and Vafa conjecture.

Topological string theory is a computable theory. The amplitudes of the closed topological string satisfy a holomorphic anomaly equation, which is a recursive differential equation. Recently this equation has been extended to the open topological string. We discuss the derivation of this open holomorphic anomaly equation. We find that open topological string amplitudes have new anomalies that spoil the recursive structure of the equation and introduce dependence on wrong moduli (such as complex structure moduli in the A-model), unless the disk one-point functions vanish. We also show that a general solution to the extended holomorphic anomaly equation for the open topological string on D-branes in a Calabi-Yau manifold, is obtained from the general solution to the holomorphic anomaly equations for the closed topological string on the same manifold, by shifting the closed string moduli by amounts proportional to the 't Hooft coupling.

An important application of closed topological string theory is the Ooguri, Strominger, and Vafa conjecture, which states that a certain black hole partition function is a product of topological and anti-topological string partition functions. However when the black hole has finite size, the relation becomes complicated. In a specific example, we find a new factorization rule in terms of a pair of functions which we interpret as the "non-perturbative' completion of the topological string partition functions.

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37

Bugden, Mark. "A Tour of T-duality: Geometric and Topological Aspects of T-dualities." Phd thesis, 2018. http://hdl.handle.net/1885/160672.

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The primary focus of this thesis is to investigate the mathematical and physical properties of spaces that are related by T-duality and its generalisations. In string theory, T-duality is a relationship between two a priori different string backgrounds which nevertheless behave identically from a physical point of view. These backgrounds can have different geometries, different fluxes, and even be topologically distinct manifolds. T-duality is a uniquely `stringy' phenomenon, since it does not occur in a theory of point particles, and together with other dualities has been incredibly useful in elucidating the nature of string theory and M-theory. There exist various generalisations of the usual T-duality, some of which are still putative, and none of which are fully understood. Some of these dualities are inspired by mathematics and some are inspired by physics. These generalisations include non-abelian T-duality, Poisson-Lie T-duality, non-isometric T-duality, and spherical T-duality. In this thesis we review T-duality and its various generalisations, studying the geometric, topological, and physical properties of spaces related by these dualities.
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38

Haghighat, Babak [Verfasser]. "On topological string theory with Calabi-Yau backgrounds / vorgelegt von Babak Haghighat." 2009. http://d-nb.info/1000529657/34.

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Krefl, Daniel [Verfasser]. "Real mirror symmetry and the real topological string / vorgelegt von Daniel Krefl." 2009. http://d-nb.info/995553556/34.

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40

Alim, Murad [Verfasser]. "Mirror symmetry, toric branes and topological string amplitudes as polynomials / vorgelegt von Murad Alim." 2009. http://d-nb.info/995734097/34.

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41

Wrase, Timm Michael 1978. "Type II flux compactifications." 2008. http://hdl.handle.net/2152/17969.

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Orientifolds of type II string theory offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NSNS and RR field strengths, but also fluxes that are T-dual to the NSNS three-form flux. These additional ingredients can help stabilize moduli and lead to D-term contributions to the effective scalar potential. We describe in general how these fluxes appear as parameters of an effective N = 1 supergravity theory in four dimensions for type IIA and type IIB string theory. We also show how these fluxes arise from compactifications on six-dimensional spaces that can be described by toroidal fibers twisted over a toroidal base. This approach leads us to a more subtle treatment of the quantization of the general NSNS fluxes. We illustrate these phenomena with examples of certain orientifolds of T⁶/Z₄.
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42

Marchal, Olivier. "Aspects géométriques et intégrables des modèles de matrices aléatoires." Thèse, 2010. http://hdl.handle.net/1866/6861.

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Cette thèse traite des aspects géométriques et d'intégrabilité associés aux modèles de matrices aléatoires. Son but est de présenter diverses applications des modèles de matrices aléatoires allant de la géométrie algébrique aux équations aux dérivées partielles des systèmes intégrables. Ces différentes applications permettent en particulier de montrer en quoi les modèles de matrices possèdent une grande richesse d'un point de vue mathématique. Ainsi, cette thèse abordera d'abord l'étude de la jonction de deux intervalles du support de la densité des valeurs propres au voisinage d'un point singulier. On montrera plus précisément en quoi ce régime limite particulier aboutit aux équations universelles de la hiérarchie de Painlevé II des systèmes intégrables. Ensuite, l'approche des polynômes (bi)-orthogonaux, introduite par Mehta pour le calcul des fonctions de partition, permettra d'énoncer des problèmes de Riemann-Hilbert et d'isomonodromies associés aux modèles de matrices, faisant ainsi le lien avec la théorie de Jimbo-Miwa-Ueno. On montrera en particulier que le cas des modèles à deux matrices hermitiens se transpose à un cas dégénéré de la théorie isomonodromique de Jimbo-Miwa-Ueno qui sera alors généralisé. La méthode des équations de boucles avec ses notions centrales de courbe spectrale et de développement topologique permettra quant à elle de faire le lien avec les invariants symplectiques de géométrie algébrique introduits récemment par Eynard et Orantin. Ce dernier point fera également l'objet d'une généralisation aux modèles de matrices non-hermitien (beta quelconque) ouvrant ainsi la voie à la ``géométrie algébrique quantique'' et à la généralisation de ces invariants symplectiques pour des courbes ``quantiques''. Enfin, une dernière partie sera consacrée aux liens étroits entre les modèles de matrices et les problèmes de combinatoire. En particulier, l'accent sera mis sur les aspects géométriques de la théorie des cordes topologiques avec la construction explicite d'un modèle de matrices aléatoires donnant le dénombrement des invariants de Gromov-Witten pour les variétés de Calabi-Yau toriques de dimension complexe trois utilisées en théorie des cordes topologiques. L'étendue des domaines abordés étant très vaste, l'objectif de la thèse est de présenter de façon la plus simple possible chacun des domaines mentionnés précédemment et d'analyser en quoi les modèles de matrices peuvent apporter une aide précieuse dans leur résolution. Le fil conducteur étant les modèles matriciels, chaque partie a été conçue pour être abordable pour un spécialiste des modèles de matrices ne connaissant pas forcément tous les domaines d'application présentés ici.
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to ``quantum algebraic geometry'' and to the generalization of symplectic invariants to ``quantum curves''. Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold. Since the range of the applications encountered is large, we try to present every domain in a simple way and explain how random matrix models can bring new insights to those fields. The common element of the thesis being matrix models, each part has been written so that readers unfamiliar with the domains of application but familiar with matrix models should be able to understand it.
Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard.
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