String theory has proved to be a valuable theoretical laboratory for probing gravity and gauge theory in a unified framework. In this thesis some of the exciting spin-offs of string theory such as branes and higher spin are studied. After a review of the basics of string theory the four papers of the thesis are discussed. In the first paper we support the equivalence between two descriptions of non-commutative open strings by calculating scattering amplitudes in both approaches. The second paper gives a physical interpretation of the fact that Ramond-Ramond charge in string theory on SU(2) is only defined modulo an integer. In the third paper we calculate contributions to the stress-energy tensor of higher-spin theory in four dimensional AdS space, and in the last paper of the thesis we compare the free energy of the two dimesional type 0A extremal blackhole and find agreement with the corresponding quantity in a deformed matrix model.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / O objetivo deste trabalho à apresentar uma extensÃo do cenÃrio Gherghetta-Shaposhnikov (GS) atravÃs da introduÃÃo de um parÃmetro adimensional em uma geometria nÃo-fatorizÃvel em seis dimensÃes, onde supomos que o nosso universo observÃvel à representado por uma 3-brana minkowskiana e as outras duas sÃo dimensÃes extras, com uma delas compacta. Neste modelo, realizamos o processo de linearizaÃÃo das equaÃÃes de Einstein fazendo uso de um mÃtodo perturbativo, a fim de encontrarmos as equaÃÃes de movimento para em seguida localizarmos o modo-zero gravitacional. A partir desses procedimentos, novos resultados foram obtidos no tocante as propriedades fÃsicas e geomÃtricas desse novo cenÃrio. Com este novo modelo sistematizamos a localizaÃÃo de gravidade em uma geometria 6-dimensional, exibindo um exemplo onde ocorre localizaÃÃo de gravidade e obtendo esse resultado atravÃs de uma extensÃo do modelo GS. / The purpose of this work is to show an expanse about Gherghetta-Shaposhnikov (GS) scenery through the introduction of a dimensionless parametric in the warped geometry in six dimensions, we suppose which our universe the way that we watch is stood for minkowskâs 3-brane and the two other are additional dimensions and one of them is compact. In that new model, we are able to achieve the linear process about Einsteinâs equation. In order to achieve a perturbation in the metric, so that we are able to locate the equation of motion, consequently finding the massless gravity model. Through these procedures, we have new results about the geometry and physics states in that new scenery. In that new scenery we order the gravity location in a 6-dimensinal geometry, in order to showing an instant where we can find the gravity location, then we get this type of location through an expansion of the GSâs model.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / As teorias de dimensÃes extras tem aplicaÃÃo em diversos ramos de FÃsica de altas energias, auxiliando no entendimento do problema de hierarquia de FÃsica de PartÃculas, nos problemas de matÃria escura e energia escura, alÃm da explicaÃÃo de novas partÃculas. O objetivo desta tese à apresentar aspectos gerais da localizaÃÃo de campos em geometrias de mundo brana nÃo fatorizÃveis warped em seis dimensÃes (6D), onde destacaremos o confinamento de campos fermiÃnicos. Iniciaremos apresentando os modelos 6D espessos e regulares desenvolvidos pelo grupo de Teoria de Campos da UFC e faremos um comparativo destes com outros modelos finos ou nÃo regulares da literatura. Compararemos tambÃm as diferenÃas que ocorrem do confinamento de campos de 5D para 6D. AlÃm disso, a localizaÃÃo dos campos bosÃnicos (gravidade, campo escalar e campo de calibre vetorial) em 6D serà tambÃm discutida. Observaremos que o modo zero da gravidade serà responsÃvel por reproduzir a lei de Newton em nosso mundo 4D. Para o tema central do confinamento de fÃrmions, detalharemos os resultados dos artigos publicados durante meu doutorado. Demonstraremos que à necessÃrio o uso de um acoplamento mÃnimo com um campo de calibre tanto para o espinor de Dirac como para o de Rarita-Schwinger em 6D, apontaremos diferentes escolhas de calibre para os diferentes modelos abordados. Seguindo, exibiremos o espinor Elko. Este espinor tem dimensÃo canÃnica de massa um em 4D (dimensÃo de massa dois em 6D), sendo um autoespinor do operador de conjugaÃÃo de carga de dual helicidade e um candidato natural à matÃria escura. Verificaremos que o Elko necessita de um acoplamento exÃtico para seu confinamento em 6D. AlÃm disso, trataremos de assuntos correlacionados, como as correÃÃes da lei de Coulomb para modelos em dimensÃes extras. Outro assunto presente na tese serà a aplicaÃÃo do conceito de Entropia Configuracional para delimitar os parÃmetros de modelos 6D.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / In this work is analysed how is the behavior of the complex scalar field in the Randall- Sundrum RS scenery. The RS model is a model of extra dimension, that solves satisfactorily the problem of the Higgs hierarchy. The problem is related to the big discrepancy between the gravitational and eletroweak scales of mass. The obtained results are based in a not factorable geometry of the Anti-de-Sitter type. We will do a review about general relativity and spacetime anti-de-sitter. We will see the construction of the models RS-I and RS-II, as well how the calculus of conections, through the Christoffel symbol, Ricci tensor, Ricci scalar and Einsteins tensor. Finally, we study the localization of the charge and current of the complex field in a brane. / Nesse trabalho à analisado como se comporta o campo escalar complexo em um cenÃrio de Randall-Sundrum (RS). O modelo RS à um modelo de dimensÃes extras, que resolve de maneira satisfatÃria o problema da hierarquia de Higgs. Esse problema diz respeito à grande discrepÃncia entre Ãs escalas de massa gravitacional e eletrofraca. Os resultados obtidos sÃo fundamentados em uma geometria nÃo-fatorizÃvel do tipo Anti-de-Sitter. Serà feita uma revisÃo sobre Relatividade Geral e EspaÃo-tempo Anti-de-Sitter. Serà visto a construÃÃo dos Modelos de RS-I e RS-II, bem como o cÃlculo das conexÃes, atravÃs do sÃmbolo de Christoffel, tensor de Ricci, escalar de Ricci e tensor de Einstein. Por fim, estudamos a localizaÃÃo da carga e da corrente do campo complexo na brana.

Orientador: Prof. Dr. Vilson Tonin Zanchin / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017. / Nesta tese exploramos alguns aspectos de teorias de campo fortemente acoplados usando o respectivo dual gravitacional. Comecamos estudando perturbacoes gravitacionais de cordas negras em rotacao num espaco-tempo assintoticamente Anti-de Sitter (AdS) em quatro dimensoes. E apresentado uma analise completa do espectro dos modos quasinormais (QNMs), interpretacoes na teoria de campos dual, quando possivel, sao exploradas. No setor escalar das perturbacoes obtemos as relacoes de dispersao na aproximacao hidrodinamica seguindo tres abordagens: perturbacoes gravitacionais, flutuacoes hidrodinamicas de um fluido relativista em (2+1) dimensoes e uma analise de vetores de onda relativistas. Os resultados obtidos no limite hodrodinamico mostram efeitos relativistas como a contracao de Lorentz, dilatacao do tempo de amortecimento e o efeito Doppler da frequencia. Os resultados numericos tambem mostram um crossover do regime hidrodinamico para o relativista e do regime nao hidrodinamico para o relativista, o ultimo para o primeiro modo nao hidrodinamico. Adicionalmente reportamos o surgimento de uma nova classe de modos quasinormais. Na segunda parte exploramos modelos fenomenologicos para a cromodinamica quantica (QCD). Primeiramente, exploramos um modelo holografico para mesons vetoriais no contexto do modelo soft-wall, exploramos o derretimento desses estados de quasiparticula quando a temperatura e adicionado atraves de um buraco negro no fundo gravitational. Tambem calculamos os modos quasinormais neste modelo e as relacoes de dispersao neste modelo. Seguimos um procedimento semelhante para explorar o derretimendo dos mesons escalares. A diferencia em relacao aos mesons vetoriais e que pode ser introduzido um dilaton quartico no regime do ultravioleta (UV) para descrever o condensado de gluons, enquanto que o comportamento linear do espectro de massas e confinamento e garantido por um dilaton quadratico no regime do infravermelho (IR). Exploramos os efeitos da escala de energia associado com o condensado de gluons no espectro e derretimento dos mesons escalares. na ultima parte apresentando um modelo holografico para descrever o setor dos gluons do Lagrangiano de Yang-Mills implementado atraves do acoplamento do campo dilaton com a metrica. Neste contexto calculamos o espectro de massas do setor escalar e tensorial do campo dos gluons. Os resultados obtidos sao consistentes com os resultados da QCD na rede. Tambem calculamos o valor esperado do vacuo (VEV) e a densidade de energia do vacuo da QCD, ambos os resultados sao resoaveis comparados com os resultados disponiveis na literatura. No final, e proposto um novo dicionario relacionando a anomalia do traco de teorias 10 de campo conforme deformadas com a anomalia do traco da QCD. Como uma consequencia nao trivial deste dicionario observamos o surgimento de uma funcao-¿À semelhante ao resultado em QCD perturbativa a dois loops. / In this thesis we explore some aspects of strongly coupled field theories using the respective gravitational duals. We start studying gravitational perturbations of rotating black strings in asymptotically Anti-de Sitter (AdS) four-dimensional spacetime. A complete analysis of the spectrum of the quasinormal modes (QNMs) is presented, interpretations in the dual field theory, when possible, are explored. In the scalar sector of the perturbations we obtain the dispersion relations in the hydrodynamic approximation following three approaches: gravitational perturbations, hydrodynamic fluctuations of a relativistic fluid in (2+1) dimensions and an analysis of relativistic wave vectors. The results obtained in the hydrodynamic limit show relativistic effects like Lorentz contraction, damping time dilation and Doppler shift of the frequency. The numerical results also show a crossover from the hydrodynamicto- relativistic regimes and from the non-hydrodynamic-to-relativistic regimes, the last for the first non-hydrodynamic quasinormal mode (QNM). Additionally we report the emergence of a new class of QNMs. In the second part we explore phenomenological models for quantum chromodynamics (QCD). Firstly we explore a holographic model for vector mesons in the context of the softwall model. We explore the melting of these quasiparticle states when the temperature is added via a black hole on the gravitational background. We also calculate the quasinormal modes and the dispersion relations in this model. We follow a similar procedure to explore the melting of scalar mesons. The difference in relation to the vector mesons case is that a quartic dilaton in the ultraviolet (UV) regime can be introduced to describe the gluon condensate, while the linear behaviour of the mass spectrum and confinement is guaranteed by a quadratic dilaton field infrared (IR) regime. We explore the effects of the energy scale associated with the gluon condensate in the mass spectrum and melting of the scalar mesons. In the last part we present a holographic model to describe the gluon sector of the Yang- Mills Lagrangian implemented through the coupling of the dilaton field to the metric. In this context we calculate the mass spectrum of the scalar and tensor sectors of the gluons field. The results obtained are consistent with lattice QCD. We also calculate the vacuum expectation value (VEV) and the energy density of the QCD vacuum, both results are reasonable compared with results currently available in the literature. At the end a new dictionary is proposed, which relates the trace anomaly of deformed conformal field theories (CFTs) to the trace anomaly of QCD. As a non trivial consequence of this dictionary we observe the emergence of a â function similar to the two loops result in perturbative QCD.

We discuss certain aspects of string field theory and its applications in exploring the land- scape of classical string theory vacua. We start by giving a brief overview of various tree-level string field theories, as well as of some relevant mathematical background. As a byproduct of our general discussion of observables, we present a new gauge-invariant quantity for the A∞ formulation of open superstring field theory. Putting particular emphasis on perturba- tive methods, we proceed to review in detail the construction of tree-level effective actions governing the dynamics of a certain subset of degrees of freedom. In light of recent devel- opments, we also discuss efficient methods for evaluating certain vertices of zero-momentum effective actions for open superstring and heterotic string field theories in the presence of a global N = 2 worldsheet superconformal symmetry. We show how to apply this perturbative approach to study dynamics of the D(−1)/D3 system (both with and without a B-field), while also discussing a number of more complicated Dp-brane configurations. At generic points in their moduli spaces, such bound states of Dp-branes clearly cannot be described in terms of simple Dirichlet or Neumann boundary conditions. The rest of this thesis is therefore devoted to developing analytic...

In den letzten Jahren hat die Erforschung von Branen zu vielen neuen Einsichten in String- und M-Theorie geführt. Ein Großteil dieser Forschung behandelte den Fall großen Volumens, wo geometrische Methoden zuverlässige Informationen liefern. Die Extrapolation in den Bereich, wo die endliche Ausdehnung des Strings wichtig wird (`stringy regime'), erfordert gewöhnlich neue Methoden aus der konformen Feldtheorie mit Randbedingungen. Branen auf Gruppenmannigfaltigkeiten ermöglichen einen guten Zugang zu diesem Problem. Obwohl sie nichttriviale Hintergründe beschreiben, was zu vielen interessanten Effekten führt, sind sie immer noch gut beherrschbar. Sie dienen auch als Bausteine bei den Restklassen- und Orbifoldkonstruktionen von im Wesentlichen allen bekannten konformen Modellen. Die vorliegende Arbeit untersucht die Dynamik von Branen auf Gruppenmannigfaltigkeiten und Restklassenmodellen. In einem bestimmten Grenzfall wird die Dynamik von nichtkommutativen Eichtheorien regiert. Viele der Prozesse lassen sich in den Bereich extrapolieren, wo Stringeffekte eine Rolle spielen. Sie äußern sich als Renormierungsgruppenflüsse auf den zweidimensionalen Weltflächentheorien mit Rändern. Solche Flüsse sind auch von Interesse in der Festkörpertheorie, wo sie Randphänomene in eindimensionalen Systemen beschreiben. Wesentliche Daten über diese dynamischen Prozesse sind in Ladungen von D-Branen kodiert. Wir werden die Resultate, die wir über Prozesse zwischen verschiedenen Brankonfigurationen erhalten, mit der Vermutung vergleichen, dass die Ladungen Werte in getwisteten K-Gruppen annehmen. / In recent years, the study of branes has led to many new insights into string and M-theory. Much of this study was done in the large-volume regime where geometric techniques provide reliable information. The extrapolation into the stringy regime usually requires new methods from boundary conformal field theory. Branes on group manifolds give us a good handle on this issue. Although they describe non-trivial backgrounds leading to many interesting effects, they are still tractable. They also serve as building blocks in the coset and orbifold constructions of essentially all known conformal models. The present thesis investigates the dynamics of branes on group manifolds and coset models. In some limiting regime, the dynamics are governed by non-commuta\-tive gauge theories. Many of the processes can be extrapolated to the stringy regime. They manifest themselves as renormalization group flows on the two-dimensional worldsheet theories with boundaries. Such flows are of interest also in condensed matter theory where they describe boundary phenomena in one-dimensional systems. Essential data on these dynamical processes are encoded in D-brane charges. We will compare the obtained results on processes between brane configurations with the conjecture that the charges take their values in twisted K-groups.

In dieser Arbeit stellen wir verschiedene Tests der (M)atrixtheorie-Vermutung vor. Die (M)atrixtheorievermutung besagt, dass die Dynamik von M-Theorie, der Urtheorie, die alle bekannten Stringtheorien und auch elfdimensionale Supergravitation als bestimmte Grenzfaelle enthalten soll, durch ein quantenmechanisches Matrixmodell gegeben ist. Insbesondere untersuchen wir Streuprozesse sowohl aus Sicht des Matrixmodells, als auch aus Sicht der Supergravitation, und vergleichen die resultierenden S-Matrixelemente. Wir finden beeindruckende Uebereinstimmung zwischen den beiden Theorien, solange wir uns auf klassische Supergravitation beschraenken. Sobald wir auch Quanteneffekte auf der Supergravitationsseite einbeziehen, hat diese Uebereinstimmung keinen Bestand. Des weiteren untersuchen wir die Frage, ob Loesungen der klassischen Matrixmodell-Bewegungsgleichungen mit Impulsuebertrag existieren, und finden eine negative Antwort. / In this thesis, we present several tests of the M(atrix)-Model conjecture that asserts that the dynamics of M-Theory, the eleven-dimensional Ur-theory containing all known string theories and also eleven-dimensional supergravity in specific limits, is given by a quantum mechanical matrix model. In particular, scattering processes are analyzed both from the M(atrix)-Model and from the supergravity perspective and the corresponding S-matrix elements are compared. We find impressive agreement between these two theories as long as only classical supergravity is considered. If one includes also quantum effects on the supergravity side, the agreement does not persist. In addition to these calculations, the question of the existence of classical solutions to the M(atrix)-Model equations of motion with momentum transfer is addressed and answered negatively.

Die vorliegende Arbeit beinhaltet ein einführendes Kapitel über Orbifold-Konstruktionen in dem neben rudimentären Grundlagen bereits speziellere Themen wie Diskrete Torsion und asymmetrische Orbifold-Gruppen behandelt werden. Als Beispiele für Orbifolde werden Kompaktifizierungen auf Tori sowie das asymmetrische T^4/Z(3)^L x Z(3)^R Orbifold behandelt. Danach wird eine allgemein gehaltene Einführung in Orientifolde gegeben, einschließlich des offenen String Sektors samt Chan-Paton Freiheitsgraden. Die darauf folgenden Kapitel 4-7 behandeln von mir durchgeführte Forschungsarbeiten. Kapitel 4 beschäftigt sich mit der Quantisierung des offenen Strings mit linearen Randbedingungen, wie sie bei Strings in elektro-magnetischen Feldern auftreten. Weiterhin wird die Quantisierung der Null- und Impuls-Moden des offenen Strings in Torus-Kompaktifizierungen durchgeführt. Außerdem wird für den Fall allgemeiner konstanter Hintergrund Neveu-Schwarz U(1)-Hintergrundfelder der Kommutator der Stringkoordinaten berechnet. Dieser stützt bisherige Resultate zur Nicht-Kommutativität von offenen Stringtheorien in Neveu-Schwarz Hintergründen. Kapitel 5 gibt, zusammen mit einigen neuen Erkenntnissen, Resultate von [1] über asymmetrische Orientifolde, insbesondere deren D-Branen Inhalt wieder. Kapitel 6 faßt die Veröffentlichung [2] zusammen, in der untersucht wurde, inwieweit sich phänomenolgisch interessante Modelle in Orientifolden von Torus-Kompaktifizierungen finden lassen. Insbesondere tragen die D9-Branen magnetische Flüsse, womit chirale Fermionen im Spektrum auftreten. Die Rechnungen werden größtenteils im gleichwertigen, T-dualen Bild ausgeführt. In diesem ist die Anzahl der chiralen Fermionen durch die topologische Schnittzahl der D-Branen gegeben. Existieren auf Torus-Kompaktifizierungen entweder nur nicht-chirale oder nicht-supersymmetrische Modelle, so lassen sich auf gewissen Orbifolden beide Eigenschaften miteinander vereinbaren. Kapitel 7 behandelt das "sigma Omega"-Orientifold auf einem T^6/Z(4) Orbifold. Als besonders interessantes Beispiel wird ein supersymmetrisches U(4) x U(2)^3_L x U(2)^3_R Modell vorgestellt, daß durch Einschalten geeigneter Hintergrundfelder in der effektiven Niederenergie-Wirkung auf ein Modell gebrochen wird, daß dem MSSM (minimalem supersymmetrischen Standard Modell) sehr ähnlich ist. Dieses Kapitel basiert auf unserer Publikation [3]. Ferner ist der Arbeit ein Anhang beigefügt, der einige der verwendeten Formeln sowie Beweise zu zwei Sätzen enthält, die im Text verwendet wurden. / This thesis contains an introductory chapter on orbifolds. Besides rudimentary basics we discuss more advanced topics like discrete torsion and asymmetric orbifold groups. As examples we investigate torus compactifications and an asymmetric T^4/Z(3)^L x Z(3)^R orbifold. The following chapter explains the foundations of orientifolds, including open strings with Chan-Paton degrees of freedom. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they show up in electro-magnetic fields. We quantize the zero- and momentum-modes for toroidal compactifications, too. As an application we calculate the commutator of the coordinate fields in the case of general constant Neveu-Schwarz U(1)-field strengths. Thereby we confirm previous results on non-commutativity of open string theories in Neveu-Schwarz backgrounds. Chapter 5 reviews the results of a former publication [1] on asymmetric orientifolds, supplemented by some recent insights in connection with the preceeding chapter. Chapter 6 is a summary of [2]. In this publication we investigated to what extend one can build phenomenologically interesting models from toroidal orientifolds. By turning on magnetic fluxes on D9-branes we induce chiral fermions. Most calculations are performed in an (equivalent) T-dual picture. Here the number of chiral fermions is given by the topological intersection number of D-branes. In orientifolds of toroidal compactifications one obtains either non-chiral or non-supersymmetric orientifold solutions. However both properties can be reconciled in orientifolds that are obtained from specific supersymmetric orbifold compactifications. In chapter 7 we present the "sigma Omega"-Orientifold on a T^6/Z(4) orbifold. As a very attractive example we investigate a supersymmetric U(4) x U(2)^3_L x U(2)^3_R model that is broken to an MSSM-like model by switching on suitable background fields in the low energy effective action. This chapter is based on our publication [3]. The thesis is supplemented by an appendix with formulas applied in the text, as well as proofs to two theorems that were used as well.

A complete non trivial supersymmetric deformation of the maximal supergravity in two dimensions is achieved by the gauging of a SO(9) group. The resulting theory describes the reduction of type IIA supergravity on an AdS_2 x S^8 background and is of first importance in the Domain-Wall / Quantum Field theory correspondence for the D0-brane case. To prepare the construction of the SO(9) gauged maximal supergravity, we focus on the eleven dimensional supergravity and the maximal supergravity in three dimensions since they give rise to important off-shell inequivalent formulations of the ungauged theory in two dimensions. The embedding tensor formalism is presented, allowing for a general desciption of the gaugings consistent with supersymmetry. The SO(9) supergravity is explicitly constructed and applications are considered. In particular, an embedding of the bosonic sector of the two-dimensional theory into type IIA supergravity is obtained. Hence, the Cartan truncation of the SO(9) supergravity is proved to be consistent. This motivated holographic applications. Therefore, correlation functions for operators in dual Matrix models are derived from the study of gravity side excitations around half BPS backgrounds. These results are fully discussed and outlooks are presented.