Diese Doktorarbeit behandelt quantentheoretische Aspekte von Typ II Superstringtheorien in AdS5xS5- und AdS4xCP3-Hintergründen für die AdS/CFT Korrespondenz. Dabei werden perturbative Methoden und Verfahren der Gitterfeldtheorie benutzt. Die Konstruktion des Supercoset-Sigma-Modell für Strings im AdS5xS5wird skizziert, während die generelle Quantendynamik des Superstring in AdS4xCP3 mit Hilfe einer dimensionaler Reduktion der Supermembrane-Wirkung in AdS4xS7 beschrieben wird. Ein manifest kovarianter Formalismus zur semi-klassischen Quantisierung von Strings um beliebige Minimalflächen in AdS5xS5 wird präsentiert, der durch die Darstellung der Fluktuationsoperatoren in Form von intrinsischen und extrinsischen Varianten der Hintergrundgeometrie erreicht wird. Eine Verallgemeinerung der Lame-Differentialgleichung zur 4. Ordnungwird mit Hilfe der Spektralmethode exakt gelöst. Dadurch konnten in 1-Schleifennäherung die Energie des String im SU(2)-Sektor, im Grenzfall beschrieben durch ein Quantum-Landau-Lifshitz-Modell, und der bosonische Beitrag zur Energie des in AdS5 und S5 rotierenden String bestimmt werden. In ähnlicher Weise erhält man in 1-Schleifennäherung den ¼-BPS-Latitude Wilson-Loop in N=4-SYM-Theorie normiert durch den ½-BPS-Loop. Das Regularisierungsschema reproduziert die Vorhersage aus supersymmetrischer Lokalisierung bis auf einen Rest, welcher diskutiert wird. Außerdem wird die Wirkung des AdS4xCP3-String, entwickelt um den null-cusp Hintergrund, studiert und die Cusp-Anomalie in 2-Schleifennäherung berechnet. Das Ergebnis stimmt mit dem vermuteten exakten Ausdruck, der ABJM-Interpolationsfunktion, überein. Schließlich wird die AdS5xS5-Superstringtheorie in AdS-Lichtkegel-Eichung diskretisiert und mit Monte-Carlo-Algorithmen Gittersimulationen bei endlicher Kopplung durchgeführt. Dabei werden die Stringwirkung, aus der mit Hilfe von AdS/CFT die null-cusp anomale Dimension von N=4 SYM extrahiert werden kann, und die Masse einer AdS Anregung bestimmt. / This thesis discusses quantum aspects of type II superstring theories in AdS5xS5 and AdS4xCP3 backgrounds relevant for the AdS/CFT correspondence, using perturbative methods at large string tension and lattice field theory techniques inspired by a work of Roiban and McKeown. We review the construction of the supercoset sigma-model for strings in the AdS5xS5 background, whereas the general quantum dynamics of the superstring in AdS4xCP3 is described by a double dimensional reduction of the supermembrane action in AdS4xS7. We present a manifestly covariant formalism for semiclassical quantization of strings around arbitrary minimal-area surfaces in AdS5xS5, expressing the fluctuation operators in terms of intrinsic and extrinsic invariants of the background geometry. We exactly solve the spectral problem for a fourth-order generalization of the Lame'' differential equation with doubly periodic coefficients in a complex variable. This calculates the one-loop energy of the (J1,J2)-string in the SU(2) sector in the limit described by a quantum Landau-Lifshitz model and the bosonic contribution to the energy of the (S,J)-string rotating in AdS5 and S5. Similar techniques calculate the 1/4-BPS latitude Wilson loops in N=4 SYM theory at one loop, normalized to the 1/2-BPS circular loop. Our regularization scheme reproduces the next-to-leading order predicted by supersymmetric localization, up to a remainder function that we discuss upon. We also study the AdS4xCP3 string action expanded around the null cusp background and compute the cusp anomaly up to two loops. This agrees with an all-loop conjectured expression of the ABJM interpolating function. We finally discretize the AdS5xS5 superstring theory in the AdS light-cone gauge and perform lattice simulations at finite coupling with a Monte Carlo algorithm. We measure the string action, from which we extract the null cusp anomalous dimension of N=4 SYM as derived from AdS/CFT, as well as the mass of an AdS excitation.

Der Gegenstand dieser Arbeit ist Bestandteil der Stringtheorie und betrifft insbesondere die geometrischen Aspekte der Realisierung von Eichtheorien innerhalb der Stringtheorie. Wir studieren die Eichtheorie von D3-Branes an verallgemeinerten Singularitaeten wie der Orbifold- oder Conifold-Singularitaet. Die Einfuehrung der sogenannten Branediamanten fuehrt auf ein konsistentes Bild. Fuer diese Klasse von Modellen wird die Wirkung der Mirrorsymmetrie diskutiert. Im zweiten Teil untersuchen wir die Feldtheorie der M5-Brane auf der Grundlage des Supereinbettungsformalismus. Das Hauptresultat dieses Kapitels ist eine explizite Identifikation der selbstdualen 3-Form mit den Parametern der komplexen Struktur des Einbettungsraumes. Das heuristische Material, das in den vorangegangenen Kapiteln angesammelt wurde, weist darauf hin, dass die Informationen, die ein supersymmetrischer 3-Zykel enthaelt, zumindest teilweise auf supersymmetrische 2-Zykel zurueckgefuehrt werden koennen. Daher studieren wir den Fall von Brane-Boxen, die durch Ueberlagerung von gewoehnlichen N=2 Systemen aus D4 und NS5-Branes gewonnen werden koennen. Diese Konfigurationen erfuellen die Bedingung des `uniform bending' und der Lift auf einen supersymmetrischen 3-Zykel kann explizit ausgefuehrt werden. Im letzten Teil konstruieren wir eine neue superkonforme N=1 Eichtheorie, die aus einer Massendeformation der N=4 SYM entsteht und eine duale Supergravitationsbeschreibung durch die AdS/CFT-Korrespondenz besitzt. / The subject of this work is part of the theory of strings and in particular concerned with geometrical aspects of the realization of gauge theory within string theory. In particular we study the gauge theory of D3-branes at generalised singularities like orbifolds and the orbifolded conifold singularities. The introduction of the so called diamonds leads to a consistent picture. The action of mirror symmetry for this class of models is discussed. In a second part the field theory of the M5-brane will be investigated on the basis of the superembedding approach. The main result here will be a rather explicit identification of the self dual three form field with the parameters of the complex structure of the embedding space. The heuristic material collected from the previous chapters states that the information contained in supersymmetric 3-cycles can be partially extracted from supersymmetric 2-cycles. Thus we study the case of brane boxes, which can be obtained by sewing together usual N=2 setups of D4 and NS5-branes. These systems satisfy the condition of uniform bending and the lift to a supersymmetric 3-cycle can be performed explicitly. In the last part a new superconformal N=1 gauge theories will be constructed which arise as certain deformations of N=4 SYM and have a dual description due to the AdS/CFT correspondence.

Diese Arbeit beschäftigt sich mit drei Aspekten der AdS/CFT-Korrespondenz, die alle einen Schritt über die klassische SUGRA-Näherung hinausgehen. Zuerst diskutieren wir den BMN Grenzfall der Korrespondenz und untersuchen insbesondere das Verhalten der quantenfeldtheoretischen Propagatoren. Dabei weisen wir nach, dass die Propagatoren im für den BMN Fall relevanten Hintergrund ebener Wellen semiklassisch (WKB) exakt beschrieben werden. Danach wird im Rahmen der AdS/CFT-Korrespondenz der Grenzfall verschwindender Kopplung der konformen Feldtheorie betrachtet. Zur technischen Vereinfachung geschieht dies für das Beispiel des O(N)-Vektormodells. Dabei wird die OPE der Vierpunktfunktionen so umgeschrieben, dass sie strukturelle Ähnlichkeit mit Witten-Diagrammen einer korrespondierenden Theorie von Strömen mit höherem Spin hat. Außerdem wird das O(N)- Vektormodell bei großem N am wechselwirkenden Infrarot-Fixpunkt untersucht. Im letzten Punkt wenden wir uns schließlich der ursprünglichen AdS/CFTDualität unter Mitnahme der nächstführenden Ordnung der 1/N-Entwicklung zu. Für die Deformationen der CFT durch relevante Doppelspur-Operatoren finden wir bei Zustandssummen und konformen Anomalien exakte Übereinstimmung zwischen direkter und AdS-seitiger indirekter Rechnung. Damit wird ein nicht trivialer Test der Korrespondenz über die SUGRA-Näherung hinaus erbracht. / This thesis deals with three corners of the AdS/CFT Correspondence that lie one step beyond the classical supergravity (SUGRA) approximation. We first explore the BMN limit of the duality and study, in particular, the behavior of field theoretic propagators in the corresponding Penrose limit. We unravel the semiclassical (WKB-) exactness of the propagators in the resulting plane wave background metric. Then, we address the limit of vanishing coupling of the conformal field theory (CFT) at large N. In the simplified scenario of Higher Spin/O(N) Vector Model duality, the conformal partial wave (CPW) expansion of scalar four-point functions are reorganized to make them suggestive of a bulk interpretation in term of a consistent truncated massless higher spin theory and their corresponding exchange Witten graphs. We also explore the connection to the interacting O(N) Vector Model at its infra-red fixed point, at leading large N. Finally, coming back to the gauge theory, we study the effect of a relevant double-trace deformations of the boundary CFT on the partition function and its dual bulk interpretation. We show how the one-loop computation in the Anti-de Sitter (AdS) space correctly reproduces the partition function and conformal anomaly of the boundary theory. In all, we get a clean test of the duality beyond the classical SUGRA approximation in the AdS bulk and at the corresponding next-to-leading 1/N order of the CFT at the conformal boundary.

In der vorliegenden Arbeit werden versteckte Symmetrien innnerhalb der N=4 supersymmetrischen Yang--Mills Theorie oder der nach der AdS/CFT Korrespondenz dualen Beschreibung durch eine String-Theorie in AdS5 x S5 besprochen. Dabei betrachten wir die Maldacena--Wilson Schleife, die sich für diese Untersuchungen besonders eignet, da ihr Vakuum-Erwartungswert für glatte Kurven nicht divergiert und die vermutete Dualität zu Streuamplituden wenigstens konzeptionell eine Möglichkeit bietet, etwaige Symmetrien zu anderen Observablen zu übertragen. Ihre Beschreibung durch Minimalflächen in AdS5 erlaubt es, Symmetrien mithilfe der Integrabilität der zugrunde liegenden klassischen String-Theorie zu konstruieren. Dieser Zugang wurde bereits in der Herleitung der Yang'schen Symmetrie der Maldacena--Wilson Schleife bei starker Kopplung sowie in der Beschreibung von Deformationen gleiches Flächeninhalts von Minimalflächen in AdS3 verwendet. Diese beiden Ergebnisse werden in der vorliegenden Arbeit miteinander verbunden und erweitert. Im Sinne einer systematischen Herangehensweise besprechen wir zunächst die Symmetriestruktur der zugrunde liegenden String-Theorie. Diese Diskussion lässt sich auf die Diskussion von String-Theorien in symmetrischen Räumen verallgemeinern. Dabei zeigt sich, dass die Symmetrie, welche die Deformationen gleiches Flächeninhalts in AdS3 erzeugt, in der Symmetriestruktur dieser Modelle eine zentrale Rolle einnimmt: Sie wirkt als Aufsteige-Operator auf den unendlich vielen erhalten Ladungen und generiert somit den Spektralparameter. Weiterhin lässt sie sich anwenden, um ausgehend von der globalen Symmetrie sämtliche Symmetrien des zugrunde liegenden Modells zu konstruieren. Sie wird daher als die Master-Symmetrie dieser Modelle bezeichnet. Zusätzlich wird die Algebra der Symmetrie-Variationen sowie der erhaltenen Ladungen ausgearbeitet. Für den konkreten Fall von Minimalflächen in AdS5 diskutieren wir die Deformation der Minimalflächenlösung für den Fall eines lichtartigen Vierecks. Diese liefert die duale Beschreibung der Streuamplitude für vier Gluonen. Damit unternehmen wir einen ersten Schritt zur Übertragung der Master-Symmetrie auf Streuamplituden. Weiterhin berechnen wir die Variation der Randkurven der Minimalflächen unter der Master- und Yang'schen Symmetrie für allgemeine, glatte Randkurven. Das Ergebnis dieser Rechnung führt auf eine Verallgemeinerung der Master-Symmetrie zu einer Variation, die von der Kopplungskonstanten abhängt und für beliebige Werte der Kopplungskonstanten eine Symmetrie der Maldacena--Wilson Schleife darstellt. Unsere Diskussion erklärt das Scheitern vorheriger Versuche, die entsprechende Symmetrie im Spezialfall von Minimalflächen in AdS3 zu schwacher Kopplung zu übertragen. Wir besprechen verschiedene Ansätze, die Yang'sche Symmetrie zu schwacher oder beliebiger Kopplung zu übertragen, schlussfolgern aber letztendlich, dass eine Yang'sche Symmetrie der Maldacena--Wilson Schleife nicht vorzuliegen scheint. Die Situation ändert sich, wenn wir Wilson Schleifen in Superräumen betrachten. Diese sind die natürlichen supersymmetrischen Erweiterungen der Maldacena--Wilson Schleife. Für die Yang'sche Invarianz ihres Vakuum-Erwartungswerts wurden wichtige Anhaltspunkte gefunden und sowohl die Beschreibung dieser Operatoren als auch der Beweis der Yang'schen Invarianz bei schwacher Kopplung wurden parallel zur Arbeit an der vorliegenden Dissertation vervollständigt. Wir diskutieren das Gegenstück zu diesem Ergebnis bei starker Kopplung. Dort wird die Wilson Schleife durch eine Minimalfläche beschrieben, welche im Superraum der Superstring-Theorie vom Typ IIB in AdS5 x S5 liegt. Der Vergleich der bei starken Kopplung etablierten Invarianz mit den entsprechenden Generatoren bei schwacher Kopplung zeigt, dass die Symmetrie-Generatoren einen lokalen Anteil enthalten, der auf nicht-triviale Weise vom Wert der Kopplungskonstanten abhängt. Zusätzlich finden wir sogenannte Bonus-Symmetrien. Diese sind die analogen Generatoren in den höheren Ordnungen zum Hyperladungs-Generator, der selbst keine Symmetrie darstellt. Wir zeigen, dass diese Symmetrien in allen höheren Ordnungen der Yang'schen Algebra vorliegen. / This thesis discusses hidden symmetries within N=4 supersymmetric Yang--Mills theory or its AdS/CFT dual, string theory in AdS5 x S5. Here, we focus on the Maldacena--Wilson loop, which is a suitable object for this study since its vacuum expectation value is finite for smooth contours and the conjectured duality to scattering amplitudes provides a conceptual path to transfer its symmetries to other observables. Its strong-coupling description via minimal surfaces in AdS5 allows to construct the symmetries from the integrability of the underlying classical string theory. This approach has been utilized before to derive a strong-coupling Yangian symmetry of the Maldacena--Wilson loop and describe equiareal deformations of minimal surfaces in AdS3. These two findings are connected and extended in the present thesis. In order to discuss the symmetries systematically, we first discuss the symmetry structure of the underlying string model. The discussion can be generalized to the discussion of generic symmetric space models. For these, we find that the symmetry which generates the equiareal deformations of minimal surfaces in AdS3 has a central role in the symmetry structure of the model: It acts as a raising operator on the infinite tower of conserved charges, thus generating the spectral parameter, and can be employed to construct all symmetry variations from the global symmetry of the model. It is thus referred to as the master symmetry of symmetric space models. Additionally, the algebra of the symmetry variations and the conserved charges is worked out. For the concrete case of minimal surfaces in AdS5, we discuss the deformation of the four-cusp solution, which provides the dual description of the four-gluon scattering amplitude. This marks the first step toward transferring the master symmetry to scattering amplitudes. Moreover, we compute the master and Yangian symmetry variations of generic, smooth boundary curves. The results leads to a coupling-dependent generalization of the master symmetry, which constitutes a symmetry of the Maldacena--Wilson loop at any value of the coupling constant. Our discussion clarifies why previous attempts to transfer the deformations of minimal surfaces in AdS3 to weak coupling were unsuccessful. We discuss several attempts to transfer the Yangian symmetry to weak or arbitrary coupling, but ultimately conclude that a Yangian symmetry of the Maldacena--Wilson loop seems not to be present. The situation changes when we consider Wilson loops in superspace, which are the natural supersymmetric generalizations of the Maldacena--Wilson loop. Substantial evidence for the Yangian invariance of their vacuum expectation value has been provided at weak coupling and the description of the operator as well as its weak-coupling Yangian invariance were subsequently established in parallel to the work on this thesis. We discuss the strong-coupling counterpart of this finding, where the Wilson loop in superspace is described by minimal surfaces in the superspace of type IIB superstring theory in AdS5 x S5. The comparison of the strong-coupling invariance derived here with the respective generators at weak coupling shows that the generators contain a local term, which depends on the coupling in a non-trivial way. Additionally, we find so-called bonus symmetry generators. These are the higher-level recurrences of the superconformal hypercharge generator, which does not provide a symmetry itself. We show that these symmetries are present in all higher levels of the Yangian.

No description available.

Submitted by FERNANDO ENRIQUE SERNA ALGARÍN null (ferse1129@gmail.com) on 2018-01-10T21:52:53Z No. of bitstreams: 1 tese.pdf: 948147 bytes, checksum: 94d535ccc424f5f4201747cae4382d6a (MD5) / Approved for entry into archive by Hellen Sayuri Sato null (hellen@ift.unesp.br) on 2018-01-12T15:54:08Z (GMT) No. of bitstreams: 1 algarin_fcs_dr_ift.pdf: 948147 bytes, checksum: 94d535ccc424f5f4201747cae4382d6a (MD5) / Made available in DSpace on 2018-01-12T15:54:08Z (GMT). No. of bitstreams: 1 algarin_fcs_dr_ift.pdf: 948147 bytes, checksum: 94d535ccc424f5f4201747cae4382d6a (MD5) Previous issue date: 2017-10-02 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Nesta tese empregamos um modelo de interação de contato que preserva simetrias para estudar estrututura hadrônica e matéria de quarks. A interação de contato é uma representação de kernels não perturbativos usados em equações de Dyson-Schwinger e Bethe-Salpeter da Cromodinâmica Quântica (QCD). A ideia básica do modelo está baseada num esquema de subtração que evita passos tradicionais no cálculo de de integrais divergentes que invariavelmente levam a violações de simetrias. Em temperatura zero, as equações de Dyson-Schwinger equation para os propagadores dos quarks u; d; s and c são resolvidas e amplitudes de estado ligado de Bethe-Salpeter, que respeitam a invariância sob translações espaço-temporais e as identidades de Ward-Takahashi associadas com simetrias globais da QCD, são obtidas para calcular as massas e as constantes de decaimento eletrofracas dos mésons pseudoscalares π; K, D e Ds e dos mésons vetorias ρ, K*, D* e Ds*. As predições do modelo estão em bom acordo com dados experimentais e da QCD na rede. Em adição, estendemos o modelo para temperaturas diferentes de zero; neste caso, o problema de violação de simetrias está restrito apenas às partes puramente divergentes porque os termos que dependem das distribuições térmicas são finitas e não requerem regularização. Finalmente, investigamos a dependência com a temperatura das contribuições das flutuações quânticas quark-π e quark-σ aos coeficientes de transporte de viscosidade de cisalhamento η e volumétrica ζ e as suas razões com a densidade de entropia s. As larguras térmicas originárias dessas fluctuações são calculadas com o formalismo de teoria de campos a temperatura finita de tempo real. Para esse cálculo, empregamos os resultados obtidos com as equações de Dyson-Schwinger e Bethe-Salpeter para a dependência com a temperatura das massas dos mésons e as contantes de acoplamento quark-méson. Os resultados para as razões η/s and ζ/s estão em bom acordo com resultados com a literatura obtidos com modelos e técnicas diferentes. Em particular, nossos resultados para η/s possuem um mínimo muito próximo ao limite inferior da conjectura AdS/CFT, η/s = 1/4π. / In thesis, a symmetry-preserving contact interaction model is used to study hadron structure and quark matter. The contact interaction is a representation of nonperturbative kernels used in Dyson-Schwinger and Bethe-Salpeter equations of Quantum Chromodynamics (QCD). The basic idea of the model is based on a subtraction scheme that avoids standard steps in the evaluation of divergent integrals that invariably lead to symmetry violation. At zero temperature, the Dyson-Schwinger equation is solved for the u; d; s and c quark propagators and the boundstate Bethe-Salpeter amplitudes respecting spacetime-translation invariance and the Ward-Green-Takahashi identities associated with global symmetries of QCD are obtained to calculate masses and electroweak decay constants of the pseudoscalar π; K, D and Ds and vector ρ, K*, D*, and Ds* mesons. The predictions of the model are in good agreement with available experimental and lattice QCD data. In addition, we extend the model to nonzero temperature; here, the problem of symmetry violation is associated only with the purely divergent parts because the effects due to the termal distributions are finite and do not need regularization. We compute the temperature dependence of the masses and decay constants of the pseudoscalar mesons considered here. Finally, we have investigated the temperature dependence of the contributions of quark-π and quark-σ quantum fluctuations to the transport coefficients of shear η and bulk ζ viscosities and their ratios to the entropy density s. The quark thermal widths originating those fluctuations are calculated with the formalism of real-time thermal field theory. For these calculations, we have used the results obtained via Dyson-Schwinger and Bethe-Salpeter equations for the temperature dependence of constituent quark and meson masses and quark-meson couplings. The results for the ratios η/s and ζ/s are in fair agreement with results of the literature obtained from different models and techniques. In particular, our result for η/s has a minimum very close to the conjectured AdS/CFT lower bound, η/s = 1/4π. / CNPq:140041/2014-1

SILVA, José Euclides Gomes da. Brane resolution em conifold com torção. 2010. 120 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2010. / Submitted by francisco lima (admir@ufc.br) on 2014-03-20T14:00:30Z No. of bitstreams: 1 2010_dis_jegdasilva.pdf: 606336 bytes, checksum: 7d1080495b039a4501073a2c1711042a (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2014-05-16T21:06:49Z (GMT) No. of bitstreams: 1 2010_dis_jegdasilva.pdf: 606336 bytes, checksum: 7d1080495b039a4501073a2c1711042a (MD5) / Made available in DSpace on 2014-05-16T21:06:49Z (GMT). No. of bitstreams: 1 2010_dis_jegdasilva.pdf: 606336 bytes, checksum: 7d1080495b039a4501073a2c1711042a (MD5) Previous issue date: 2010 / We will study a technique for smoothing a naked singularity in a conifold called Brane Resolution On the one hand the singularity appears as a brane solution of supergravity containing only terms of sector Neveu-Schwarz On the other hand we can see the singularity of the conifold as coming from a fixed point of the discrete symmetry group responsible for generating the conifold The conifold is of most importance in the process of compactification in string theories in particular in so-called conical transitions In fact there are different kinds Calabi-Yau varieties that can be built Despite such spaces have distint topological characteristics it can become a space on the other transitions through conical transitions This is done through the generation of singularities in Calabi-Yau that surprisingly does not generate quantum problems. The technique consists of adding a topological term sector Ramond-Ramond action to the inclusion of a Chern-Simons term responsible for interaction between the fields of the Ramond-Ramond sector (Cn), generates a flow field and H3 = DB2 F3 = DC2 on the singularity of the conifold. From the equation of motion of the field and an appropriate choice for the configuration of the metric and fields find the warp factors that are responsible for the removal of the singularity method can also be understood topologically as the incision of a sphere in the vicinity of the place node of the cone The behavior of fields on the conifold is done in order to extend the correspondence AdS-CFT correspondence was originally proposed for the space AdS5 × S 5 but soon emerged as extensions using other varieties M4 × C6 Near the natural perity space can be written as AdS5 5 × X 5 where X is the base of the conifold space usually takes up the space base as a homogeneous space of Ricci-flat Einstein where X = 5 SU (3) / SU (2) × SU (2). However, to maintain conformal invariance of the theory of dual fields is necessary to soften the conifold through incisions of the Eguchi-Hanson type that can be of two types: a 3-sphere S 3 is called deformation or by a 2-sphere S 2 is called resolution Recently it has been proposed resolutions conifold in a scenario of heterotic theory endowed with torsion Such an effect is relevant in theories where the black hole type solutions exist in the internal variety as the branes and spinning black branes latter takes into account the black hole's angular momentum - spin - and it is a solution of Kerr From the transgression of the Bianchi identity for the 3-form field strength of the Kalb-Ramond term derived from a Gauss-Bonnet and instanton can introduce a twist and hence a new term not dependent on the connection meter. We will study the effects of such terms on conifold a smoothing compared with the case without torsion Furthermore we study the effect that another term has topological branes on the resolution of the term BF This term originated as an extension of the Chern-Simons term to four dimensions with topologically generate mass function as gauge fields for this work, we modify the action of the heterotic theory in order to obtain the term BF as one of the terms fault and then responsible for the flow that removes the singularity found for an ansatz well known a configuration where the flow generated by the BF term is responsible for resolution / Estudaremos uma técnica de suavização de uma singularidade nua em um conifold chamada Brane Resolution Por um lado a singularidade aparece como uma solução de brana de supergravidade contendo apenas termos do setor de Neveu-Schwarz Por outro lado podemos ver a singularidade do conifold como oriunda de um ponto fixo do grupo de simetria discreto responsável pela geração do conifold O conifold tem bastante importância no processo de compactificação em teorias de cordas em particular nas chamadas transições cônicas De fato existem diferentes tipos de espaços deCalabi-Yau que podem ser variedades internas Apesar de tais espaços terem características to- pológicas distintas pode-se transformar um espaço no outro através das transições cônicas Isso se faz através da geração de singularidades no espaço de Calabi-Yau que surpreendentemente não gera problemas quânticos. A técnica consiste em acrescentar um termo topológico do setor de Ramond-Ramond à ação A inclusão de um termo de Chern-Simons responsável pela interação entre os campos do setor de Ramond-Ramond (Cn ), gera um fluxo dos campos H3 = dB2 e F3 = dC2 sobre a singularidade do conifold. A partir da equação de movimento do campo pode-se, dado uma escolha adequada para a configuração da métrica e dos campos, encontrar os fatores de warp que são responsáveis pela retirada da singularidade O método também pode ser entendido topologicamente como a incisão de uma esfera no lugar da vizinhança do nodo do cone O estudo do comportamento de campos sobre o conifold é feito no intuito de extender a correspondência AdS-CFT originalmente a correspondência foi proposta para o espaço AdS5 ×S 5 mas logo surgiram extensões utilizando outras variedades como M4 × C6 Próximo a singula- ridade o espaço pode ser escrito como AdS5 × X 5 onde X 5 é o espaço base do conifold Geralmente toma-se o espaço base como um espaço homogêneo de Einstein Ricci-plana onde X 5 = SU (3)/SU (2) × SU (2). Contudo, para manter a invariância conforme da teoria de campos dual é necessário suavizar o conifold através de incisões do tipo Eguchi-Hanson que podem ser de dois tipos: por uma 3-esfera S 3 é chamada deformation ou por uma 2-esfera S 2 é chamada resolution Recentemente foram propostas resoluções do conifold em um cenário de teoria heterótica dotada de torção Tal efeito é relevante em teorias onde soluções do tipo buraco negro existem na variedade interna como as black branes e spinning branes esta última leva em conta o momento angular do buraco negro - spin - e é uma solução do tipo Kerr A partir da transgressão da identidade de Bianchi para a 3-forma intensidade de campo de Kalb-Ramond oriundo de um termo de Gauss-Bonnet e de instanton podemos introduzir uma torção e com isso um novo termo na conexão não dependente da métrica. Estudaremos os efeitos de tais termos sobre a suavização de um conifold comparando com o caso sem torção Além disso buscamos estudar o efeito que um outro termo topológico tem sobre a resolução de branas o termo BF Tal termo surgiu como uma extensão do termo de Chern-Simons para quatro dimensões tendo como função gerar massa topologicamente para campos de calibre Nesse trabalho iremos modificar a ação da teoria heterótica de modo a obtermos o termo BF como um dos termos de anomalia e logo responsável pelo fluxo que retira a singularidade Encontramos para um ansatz bastante conhecido uma configuração onde o fluxo gerado pelo termo BF é o responsável pela desingularização do espaço

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The electromagnetic and gravitational quasinormal mode spectra of plane-symmetric anti-de Sitter black holes are investigated in the present work. According to the AdS/CFT correspondence, the black hole quasinormal frequencies correspond to the poles of R-current and stress-energy tensor correlation functions in the holographically dual field theory: the N = 8 super-Yang-Mills in 2 + 1 dimensions. In the present study, this duality is explored in order to choose the quasinormal mode boundary conditions and the gauge invariant variables governing the black hole perturbations. Among the main results, it is shown that zero wavenumber axial perturbations yield only small rotations on the system, while the polar perturbations lead to a change in the mass of the black hole and may also produce cylindrical gravitational waves. In relation to the quasinormal spectra, the long-distance and low-frequency limit of the dispersion relations present the hydrodynamical behavior that is characteristic of a conformally invariant theory, with diffusion, shear and sound-wave modes. In the electromagnetic perturbation sector, it also appears purely damped modes that tend to the bosonic Matsubara frequencies in the long-wavelength regime. / No presente trabalho, investigou-se o espectro de vibrações eletromagnéticas e gravitacionais de buracos negros anti-de Sitter com horizontes plano-simétricos. Segundo a correspond ência AdS/CFT, os modos quase-normais desses buracos negros estão associados aos pólos de funções de correlação de corrente-R e do tensor energia-momento na teoria de campos holograficamente dual: a super-Yang-Mills N = 8 em 2 + 1 dimensões. Neste estudo, a relação com a teoria de campos foi explorada ao se fixar as condições de contorno que definem os modos quase-normais, bem como na escolha das quantidades invariantes de calibre que governam as perturbações dos buracos negros anti-de Sitter. Para obter as equações de onda gravitacionais, foram utilizados formalismos baseados em variações da métrica e dos escalares de curvatura de Weyl. Entre outros resultados, mostrou-se que as perturbações axiais com número de onda nulo produzem somente pequenas rotações sobre o sistema, enquanto que as perturbações polares conduzem a mudanças na massa e também podem se propagar na forma de ondas gravitacionais cilíndricas. Em relação ao espectro quase-normal, no limite de baixas freqüências e grandes comprimentos de onda, algumas relações de dispersão apresentam o comportamento hidrodinâmico característico de uma teoria conformemente invariante, com o aparecimento de modos de difusão, cisalhamento e de onda sonora. Por fim, no setor eletromagnético das perturbações, surgem também modos puramente amortecidos que tendem às freqüências de Matsubara de um sistema bosônico no regime de grandes comprimentos de onda.

This thesis consists in a self-contained study of gauge/gravity dualities in the line of the Klebanov-Witten model. Here we explore first the known Maldacena duality that relates N=4 SYM theory in four dimensions to type IIB supergravity on AdS_5×S^5 in reasonable detail, after some necessary preliminaries on supersymmetric gauge theories, where we display in detail the supersymmetry algebra and representations for N 1 supersymmetry. There we also construct the so-called superfields that will be helpful to write invariant lagrangians for gauge theoriesmreadily, and then useful to construct the gauge theory side of the Klebanov-Witten model. In the original AdS/CFT correspondence and its phenomenologically interesting extensions, Dp-branes as solutions of supergravity and nonperturbative objects in string theory where gauge theory lives are crucial. So, to preserve the self-contained nature of this work, we include a brief review of superstring theory addressed to understand the need to include this higher-dimensional objects by T-duality and, at low-energy limit of the string theory, as solutions of the Einstein equations. The first climax of this work occurs when we use all we learned to establish the Maldacena conjecture, N=4 SU(Nc) SYM theory we study in the supersymmetry chapter, living on the four-dimensional worldvolume of a stack of Nc D3-branes in a flat-space, corresponds exactly to type IIB supergravity on AdS_5×S^5 .In order to prove it, we match symmetries and operators with states in both sides. But actually this corresponds to the weak form of the correspondence, because it is not possible to handle neither string theory or gauge theory at strong coupling. The focus and main motive to have to learn the first hundred of pages here will be to extend the dual gauge theory we studied in AdS/CFT towards more realistic gauge theories as duals of some supergravity theory. The Klebanov-Witten model, consists in replacing the five-sphere in the gravity background of type IIB for a more interesting Einstein manifold X5 , a coset space called T^1,1 .The resulting dual gauge theory is expected to be less supersymmetric, and it is indeed N = 1 superconformal field theory with matter content in the bifundamental representation of the gauge group SU(N)×SU(N), and a quartic superpotential that exhibits SU(2)×SU(2)×U(1) global symmetry, which is precisely the symmetry of the coset space in the gravity side. This is not the end of the story, the Klebanov-Witten model extended the Maldacena correspondence and found as a dual gauge theory a less supersymmetric but still conformal theory. Breaking of the conformal theory, proposed by Klebanov, Nekrasov and Tseytlin, is achieved by introducing fractional M D3-branes in addition to the N regular D3-branes. The resulting theory is an SU(N+M)×SU(N) gauge theory with N = 1 supersymmetry, no longer conformal and then a little more interesting as a part of the crusade to find a QCD-like theory. This is still not the end, the last model suffers from a singularity in the deep IR, rendering the gravitational description invalid in that regime. It was conjectured that the strong dynamics of the gauge theory should somehow resolve this problem. Klebanov, again, and Strassler showed that this conjecture was correct, and argue that the RG flow is in fact an infinite series of Seiberg duality transformations- a cascade - in which the number of colors repeatedly drops from N NM , so the gaugegroup changes from SU(N+M)×SU(N) to SU(NM) ×SU(N). This process can be repeated until the IR limit where the gauge group simply becomes SU(M). So, at the end we get a N=1 SU(M) gauge theory, a QCD-like theory. We say that the standard model itself may lie at the base of a duality cascade. / Essa tese consiste num estudo autocontido das dualidades calibre/gravidade na linha do modelo do Klebanov-Witten. Aqui nos exploramos primeiro de um jeito razoavelmente detalhado,a conhecida dualidade do Maldacena que relaciona a teoria N=4 SYM em quatro dimensões com as supercordas tipo IIB no espaço AdS_5×S^5, depois de alguns preliminares necessários sobre teorias supersimétricas de calibre, onde nós mostramos em detalhe à algebra supersimétrica e as representações para N 1 supersimetria. Nós também construímos os conhecidos supercampos que são úteis para escrever lagrangianas invariantes para teorias de calibre facilmente, e então serão úteis para construir a teoría de calibre do modelo de Klebanov-Witten. Na correspondência AdS/CFT original e as suas extensões fenomenologicamente interessantes, as Dp-branas, como soluções de supergravidade e objetos não perturbativos na teoria de cordas onde as teorias de calibre moram, são essenciais. Assim ,a fim de preservar a natureza autocontida desse trabalho, nós incluímos uma breve revisão sobre teoria de supercordas dirigida a entender a necessidade de incluir esses objetos extra-dimensionais usando dualidade-T e, no limite de baixa-energia da teoria de cordas, como soluções das equações de Einstein. O primeiro clímax desse trabalho ocorre quando nós usamos tudo o que aprendemos para estabelecer a conjectura do Maldacena, a teoria de calibre N=4 SYM que nós estudamos no capítulo de supersimetria, morando no volume de mundo quadridimensional de uma pilha de Nc D3-branas (sim, o subscrito c significa cor!) em espaço plano, corresponde exatamente à teoria de supergravidade tipo IIB no espaço AdS_5×S^5 . A fim de testar ela, nós identificamos simetrias e operadores com estados em ambos lados da dualidade. Mas na verdade isto corresponde à forma fraca da correspondência, porque não é possível lidar nem com a teoria de cordas nem com a teoria de calibre no limite de acoplamento forte. O foco e motivo principal de porque nós temos que aprender as primeiras cem páginas aqui, será estender a teoria de calibre dual que estudamos em AdS/CFT, para teorias de calibre mais realisticas como duais de alguma teoria de supergravidade. O modelo do Klebanov-Witten, consiste em substituir a esfera de cinco dimensões no fundo de supergravidade da teoria de supercordas tipo IIB por um espaço que é mais interessante X5, um espaço coset chamado T^1,1. Nós esperamos que a teoria de calibre dual que resulta é menos supersimetrica, e na verdade é N =1 superconforme com um conteúdo de matéria na representação bifundamental do grupo de calibre SU(N)×SU(N), e um superpotencial quártico que tem simetria global SU(2)×SU(2)×U(1), que é precisamente a simetria do espaço coset no lado da gravidade. Mas isso não é tudo, o modelo do Klebanov-Witten estendeu a correspondência do Maldacena e encontrou como teoria dual uma teoria menos supersimetrica mas ainda conforme. A quebra da simetria conforme, proposta pelo Klebanov, Nekrasov e Tseytlin, é obtida introduzindo M D3-branas fracionais além das N D3-branas regulares. A teoria resultante é uma teoria de calibre SU(N+M)×SU(N) com N = 1 supersimetria, não mais conforme e então um pouco mais interessante como parte da nossa cruzada para encontrar uma teoria tipo-QCD. Isso ainda não é o final, o modelo anterior sofre de uma singularidade no IR profundo, tornando inválido a descrição gravitacional. Foi conjeturado então que a dinâmica do acoplamento forte na teoria de gauge deveria de algum jeito resolver esse problema. Klebanov, de novo, e Strassler mostraram que essa conjetura foi correta, e argumentaram que o fluxo do GR é de fato uma serie infinita de transformações de dualidade de Seiberg - uma cascata - onde o numero de cores cai repetidamente de NNM, e o grupo de calibre muda de SU(N+M)×SU(N) a SU(NM)×SU(N). O processo pode ser repetido até o limite IV onde o grupo de calibre simplesmente torna-se SU(M). Então, no final nós obtemos uma N = 1 teoria de calibre SU (M ), ou seja uma teoria tipo-QCD. Então, nós dissemos que o modelo padrão mesmo pode se situar na base da cascata de dualidade.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Estudaremos uma tÃcnica de suavizaÃÃo de uma singularidade nua em um conifold chamada Brane Resolution Por um lado a singularidade aparece como uma soluÃÃo de brana de supergravidade contendo apenas termos do setor de Neveu-Schwarz Por outro lado podemos ver a singularidade do conifold como oriunda de um ponto fixo do grupo de simetria discreto responsÃvel pela geraÃÃo do conifold O conifold tem bastante importÃncia no processo de compactificaÃÃo em teorias de cordas em particular nas chamadas transiÃÃes cÃnicas De fato existem diferentes tipos de espaÃos deCalabi-Yau que podem ser variedades internas Apesar de tais espaÃos terem caracterÃsticas to- polÃgicas distintas pode-se transformar um espaÃo no outro atravÃs das transiÃÃes cÃnicas Isso se faz atravÃs da geraÃÃo de singularidades no espaÃo de Calabi-Yau que surpreendentemente nÃo gera problemas quÃnticos. A tÃcnica consiste em acrescentar um termo topolÃgico do setor de Ramond-Ramond à aÃÃo A inclusÃo de um termo de Chern-Simons responsÃvel pela interaÃÃo entre os campos do setor de Ramond-Ramond (Cn ), gera um fluxo dos campos H3 = dB2 e F3 = dC2 sobre a singularidade do conifold. A partir da equaÃÃo de movimento do campo pode-se, dado uma escolha adequada para a configuraÃÃo da mÃtrica e dos campos, encontrar os fatores de warp que sÃo responsÃveis pela retirada da singularidade O mÃtodo tambÃm pode ser entendido topologicamente como a incisÃo de uma esfera no lugar da vizinhanÃa do nodo do cone O estudo do comportamento de campos sobre o conifold à feito no intuito de extender a correspondÃncia AdS-CFT originalmente a correspondÃncia foi proposta para o espaÃo AdS5 ÃS 5 mas logo surgiram extensÃes utilizando outras variedades como M4 à C6 PrÃximo a singula- ridade o espaÃo pode ser escrito como AdS5 à X 5 onde X 5 à o espaÃo base do conifold Geralmente toma-se o espaÃo base como um espaÃo homogÃneo de Einstein Ricci-plana onde X 5 = SU (3)/SU (2) à SU (2). Contudo, para manter a invariÃncia conforme da teoria de campos dual à necessÃrio suavizar o conifold atravÃs de incisÃes do tipo Eguchi-Hanson que podem ser de dois tipos: por uma 3-esfera S 3 à chamada deformation ou por uma 2-esfera S 2 à chamada resolution Recentemente foram propostas resoluÃÃes do conifold em um cenÃrio de teoria heterÃtica dotada de torÃÃo Tal efeito à relevante em teorias onde soluÃÃes do tipo buraco negro existem na variedade interna como as black branes e spinning branes esta Ãltima leva em conta o momento angular do buraco negro - spin - e à uma soluÃÃo do tipo Kerr A partir da transgressÃo da identidade de Bianchi para a 3-forma intensidade de campo de Kalb-Ramond oriundo de um termo de Gauss-Bonnet e de instanton podemos introduzir uma torÃÃo e com isso um novo termo na conexÃo nÃo dependente da mÃtrica. Estudaremos os efeitos de tais termos sobre a suavizaÃÃo de um conifold comparando com o caso sem torÃÃo AlÃm disso buscamos estudar o efeito que um outro termo topolÃgico tem sobre a resoluÃÃo de branas o termo BF Tal termo surgiu como uma extensÃo do termo de Chern-Simons para quatro dimensÃes tendo como funÃÃo gerar massa topologicamente para campos de calibre Nesse trabalho iremos modificar a aÃÃo da teoria heterÃtica de modo a obtermos o termo BF como um dos termos de anomalia e logo responsÃvel pelo fluxo que retira a singularidade Encontramos para um ansatz bastante conhecido uma configuraÃÃo onde o fluxo gerado pelo termo BF à o responsÃvel pela desingularizaÃÃo do espaÃo / We will study a technique for smoothing a naked singularity in a conifold called Brane Resolution On the one hand the singularity appears as a brane solution of supergravity containing only terms of sector Neveu-Schwarz On the other hand we can see the singularity of the conifold as coming from a fixed point of the discrete symmetry group responsible for generating the conifold The conifold is of most importance in the process of compactification in string theories in particular in so-called conical transitions In fact there are different kinds Calabi-Yau varieties that can be built Despite such spaces have distint topological characteristics it can become a space on the other transitions through conical transitions This is done through the generation of singularities in Calabi-Yau that surprisingly does not generate quantum problems. The technique consists of adding a topological term sector Ramond-Ramond action to the inclusion of a Chern-Simons term responsible for interaction between the fields of the Ramond-Ramond sector (Cn), generates a flow field and H3 = DB2 F3 = DC2 on the singularity of the conifold. From the equation of motion of the field and an appropriate choice for the configuration of the metric and fields find the warp factors that are responsible for the removal of the singularity method can also be understood topologically as the incision of a sphere in the vicinity of the place node of the cone The behavior of fields on the conifold is done in order to extend the correspondence AdS-CFT correspondence was originally proposed for the space AdS5 à S 5 but soon emerged as extensions using other varieties M4 à C6 Near the natural perity space can be written as AdS5 5 à X 5 where X is the base of the conifold space usually takes up the space base as a homogeneous space of Ricci-flat Einstein where X = 5 SU (3) / SU (2) à SU (2). However, to maintain conformal invariance of the theory of dual fields is necessary to soften the conifold through incisions of the Eguchi-Hanson type that can be of two types: a 3-sphere S 3 is called deformation or by a 2-sphere S 2 is called resolution Recently it has been proposed resolutions conifold in a scenario of heterotic theory endowed with torsion Such an effect is relevant in theories where the black hole type solutions exist in the internal variety as the branes and spinning black branes latter takes into account the black hole's angular momentum - spin - and it is a solution of Kerr From the transgression of the Bianchi identity for the 3-form field strength of the Kalb-Ramond term derived from a Gauss-Bonnet and instanton can introduce a twist and hence a new term not dependent on the connection meter. We will study the effects of such terms on conifold a smoothing compared with the case without torsion Furthermore we study the effect that another term has topological branes on the resolution of the term BF This term originated as an extension of the Chern-Simons term to four dimensions with topologically generate mass function as gauge fields for this work, we modify the action of the heterotic theory in order to obtain the term BF as one of the terms fault and then responsible for the flow that removes the singularity found for an ansatz well known a configuration where the flow generated by the BF term is responsible for resolution