Orientador: Prof. Dr. Roldão da Rocha Junior / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015. / Revisaremos principalmente modelos de mundos branas em cinco dimensões desde suas ver- sões .nas ou espessas. Em branas .nas revisaremos a formulação de Shiromizu, Maeda e Sasaki e deduziremos as Equações de Einstein efetivas na brana. Veremos que a partir delas podemos veri.car desvios na Relatividade Geral 4D devido à dimensão extra. Analisaremos as implicações diretas na teoria de buracos negros e em alguns aspectos da cosmologia. Ver- emos também um método de expansão que nos permite veri.car a extensão do horizonte de eventos ao bulk, para então introduzirmos cordas negras usando a formulação de Shiromizu, Maeda e Sasaki. Através do método mencionado, mostraremos alguns exemplos que en- volvem dois de nossos trabalhos realizados no período de doutorado. Mostraremos ainda um estudo alternativo que visa analisar as singularidades físicas no bulk oriundas de soluções de colapsos na brana. Referente às branas espessas, faremos uma revisão do modelo canônico visando o estudo de sua estabilidade. Posteriormente, iremos trabalhar a estabilidade do modelo de brana taquiônica. Nesse caso, ainda não se havia veri.cado a estabilidade para o setor de .utuações escalares de maneira geral, mas apenas na aproximação de rolamento lento. Esse resultado é então obtido pela primeira vez. Segue que uma forma de veri.car a estabilidade é observar o espectro das perturbações. Podemos então fazer uso de operadores supersimétricos, que garantem que o espectro é positivo de.nido. Nosso intuito será então veri.car a estabilidade das branas taquiônicas sem qualquer aproximação. Para isso desenvolveremos um mecanismo que envolve operadores supersimétricos de maneira não trivial, sendo uma generalização da literatura pré-existente. O principal resultado obtido é que a brana taquiônica, podendo ela ser de Minkowski ou (anti-) de Siter, é estável diante perturbações escalares. / We will review braneworlds models in .ve dimensions, such as the thin and thick branes cases. In the thin branes context we will review the Shiromizu-Maeda-Sasaki formulation and then we must obtain the e¤ective Einstein equations on the brane. Starting from these equations, we will check some deviations of 4D General Relativity, driven by extra dimension. Some of direct implications will be analyzed for black holes and cosmology. With a perturbative method that provides the event horizon in the bulk, we will introduce the notion of black string in Shiromizu-Maeda-Sasaki formulation. Across of expansion method we will analyze some examples, such as two of our works and then we must .nish with an alternative method for the treatment of singularities on the bulk. Regarding the thick brane, initially we will work the canonical model and posteriorly the tachyon brane model. In the two cases we will develop the stability of models. For the tachyon brane case, the scalar sector has not been studied but only at a slow roll approxima- tion and thus our result is original. The spectra of linear perturbations allows us the study of stability. The use of supersymmetric operators assures us a positive de.ned spectrum. The main objective of this thesis is to check the tachyon brane stability without any ap- proximation. For this purpose we will construct a nontrivial mecanism via supersymmetric operators, which is a generalization of previous literature. The signi.cant result is that the Minkowski, (anti-) de Siter tachyon brane remains stable when perturbed by scalar sector.

This thesis is concerned with several problems in general relativity and low energy string theory that are pertinent to the time evolution of the gravitational field. We present a formulation of the Einstein field equations in terms of variational techniques borrowed from geometric analysis. These equations yield the evolution equations for the Cauchy problems of both general relativity and low energy string theory. We then proceed to investigate the evolutionary linear stability of Schwarzschild-like solutions in higher dimensional relativity called black strings. These objects are determined to be linearly unstable. This motivates a further stability analysis of the charged p-brane solutions of low energy string theory. We show that one can eliminate linear instabilities in p-branes for sufficiently large values of charge. We also consider the characteristic problem of general relativistic magnetohydrodynamics (GRMHD). We compute the eigenvalues and eigenvectors of GRMHD and establish degeneracy conditions. Finally, we consider the initial value problem for axisymmetric GRMHD. We formulate the general Einstein and MHD equations under the assumption of a stationary axisymmetric spacetime without assuming the circularity condition.

<p>The purpose of this thesis is twofold and motivated by recent developments in string theory and extra dimensional models. The first objective is to describe the development and progress in the codimension-2 brane paradigm as a potential cosmological scenario. Secondly, it presents the Antide Sitter/Conformal Field Theory (AdS/CFT) conjecture, also known as holography, as a tool for calculating physical quantities in condensed matter system and goes on to model the quantum Hall effect. We first describe the initial development of treating back-reaction in codimension-2 branes systems with a scalar and gauge field. The purpose of this is to examine the low-energy effective dynamics on the brane. Furthermore, applications are then explored for D7-branes in F-theory as well as D3-branes in large extra dimensional scenarios explored as a model for the cosmological constant problem. The result of this work is that the higher and lower dimensional scenarios are consistent with each other once brane back-reaction is considered in these models. This work led to a number of future works one of which is in relation to the cosmological constant problem. While the subsequent work is beyond the scope of this thesis, we present a picture and further references for the reader. The larger, later, portion of this thesis introduces the concept of holography, its origins, and the applicability to condensed matter systems. Furthermore, we discuss the applicability in particular to the quantum Hall effect (QHE) and present a model in the holographic language that correctly reproduces some of the physics of the QHE. This includes a paper in which we introduce the model, along with demonstration of symmetry properties and conductivity calculations, as well as a paper which examines the finite size scaling behaviour of the model. As a benefit to the reader, we present a `starter edition guide' to the AdS/CFT dictionary preceding these papers for non-experts such that this thesis is self-contained. The upshot is that these avenues of work, in particular quantum Hall-ography, have been very successful in modeling physics using tools originally developed by string theory. As such, it provides support for string theory as a model and framework, as well as providing more opportunities for future predictions of physical quantities.</p> / Doctor of Philosophy (PhD)

Cette thèse s'attache à comprendre le rôle du champ de fond antisymétrique B en théorie des cordes. Nouveauté essentielle et prometteuse par rapport à la théorie des champs, puisqu'il accompagne naturellement la courbure de l'espace-temps g, son importance a été soulignée ces dernières années dans différents domaines, auxquels j'ai tenté de contribuer. Le premier chapitre étudie la transformation de Seiberg-Witten, qui relie des branes ordinaires plongées dans un champ B à des branes non-commutatives. A la recherche d'une expression explicite sur le secteur de jauge, il tente d'en éclaircir la signification. Le chapitre 2 s'attaque à la dynamique non abélienne des branes M5 en M-théorie. Par différentes approches, supersymétrique ou plus géométrique, je tente d'y proposer un contenu en champs pour un paquet de N M5-branes, expliquant leur anomalie en N^3. Ces champs formeraient alors une version non-abélienne des théories de jauge à connexion tensorielle. Enfin, la présence d'un champ B autorise des variétés de compactification plus générales que les espaces de Calabi-Yau, dites variétés à structure SU(3). La symétrie-miroir peut être étendue dans ce cadre, en la décrivant comme une T-dualité le long d'une fibration toroïdale. Sa description géométrique met alors en jeu les composantes de la torsion intrinsèque, qui sont mélangées à celles de la courbure H=dB, ainsi que je le détaille dans le chapitre 3.

<p>For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level.</p><p>A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only.</p><p>We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.</p>

<p>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.</p>

For the first time in the history of physics we stand in front of a theory that might actually serve as a unification of it all - string theory. It provides a self-consistent framework for gravity and quantum mechanics, which naturally incorporates matter and gauge interactions of the type seen in the standard model. Unfortunately, at the moment we do not know of any principle that selects the vacuum of the theory, so predictions about our four-dimensional world are still absent. However, the introduction of extended objects opens up an intricate new arena of physics, which is non-trivial and challenging to map out, even at a basic level. A key concept of quantum gravity is holography; this is realised in string theory by the AdS/CFT correspondence, which relates string theory to a field theory living in a lower dimensional space. In this thesis we discuss two limits of the correspondence, namely the BMN limit, giving rise to a plane wave geometry, and the tensionless limit, exhibiting massless higher spin interactions. We also study a limit of string theory in a background electric field, where the theory is described by open strings and positively wound closed strings only. We begin with a brief review of the theory, focusing on an intuitive understanding of the basic aspects and serving as an introduction to the papers. In the first paper we calculate, from two different points of view, scattering amplitudes in the non-commutative open string limit. In the second paper we obtain the quadratic scalar field contributions to the stress-energy tensor in the minimal bosonic higher spin gauge theory in four dimensions. In the last paper we propose a way to avoid fermion doubling when discretizing the string in the BMN limit.

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.