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.

Kaluza-Klein theories generally in $(4+D)$ and more specifically in five dimensions are reviewed. The magnetic monopole solutions found in the Kaluza-Klein theories are generally reviewed and their generalizations to Anti-de Sitter spacetimes are discussed.

Un problema clásico en geometría lorentziana es la descripción de las inmersiones isométricas entre los espacios lorentzianos de curvatura constante. En este trabajo nos centramos en la clasificación de las inmersiones isométricas del plano lorentziano en el espacio anti-de Sitter tridimensional. Damos una fórmula de representación de estas inmersiones en términos de pares de curvas (con posibles singularidades) en el plano hiperbólico. Esto nos permite resolver los problemas propuestos por Dajczer y Nomizu en 1981. De entre todas las inmersiones isométricas del plano lorentziano en el espacio anti-de Sitter, algunas de ellas corresponden a toros lorentzianos (los ejemplos más sencillos son los toros de Hopf). Como aplicación de nuestra anterior descripción, probamos que todos estos toros pueden obtenerse a partir de dos curvas cerradas en el espacio hiperbólico. Finalmente, demostramos que los toros de Hopf son los únicos toros llanos lorentzianos inmersos en una amplia familia de sumersiones de Killing lorentzianas tridimensionales. / A classical problem in Lorentzian geometry is the description of the isometric immersions between Lorentzian spaces of constant curvature. We investigate the problem of classifying the isometric immersion from the Lorentz plane into the three-dimensional anti-de Sitter space, providing a representation formula of these isometric immersions in terms of pairs of curves (possibly with singularities) in the hyperbolic plane. We then give an answer to the open problems proposed by Dajczer and Nomizu in 1981. Among all isometric immersions of the Lorentz plane into the anti-de Sitter space, some of them are actually Lorentzian tori (the basic examples are the Hopf tori). As an application of our previous description, we prove that any such torus can be recovered from two closed curves in the hyperbolic plane. Finally, we prove that Lorentzian Hopf tori are the only immersed Lorentzian flat tori in a wide family of Lorentzian three-dimensional Killing submersions.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T13:00:44Z No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) / Made available in DSpace on 2017-09-12T13:00:44Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) Previous issue date: 2016-02-25 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this thesis, we study the influence of gravitating non-Abelian cosmic strings on the spacetime geomerty. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically to determine the behaviour for the Higgs, gauge and metric fields. This model under consideration present two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling. So, we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as function of the energy scale where the gauge symmetry is spontaneously broken. We have extented this analysis to de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also for the metric tensor for specific values of the physical parameters of the theory. For de Sitter case, we find the appearance of horizons that although being consequence of the presence of the cosmological constant it strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (tt) and (zz) components of the metric tensor. They present a strongly increasing for large distance from the string. / Nesta tese estudamos a influência das cordas cósmicas não-Abelianas na geometria do espaço-tempo. Para este fim, utilizamos um modelo de Higgs não-Abeliano acoplado com a gravidade e obtemos um sistema de equações diferenciais não-lineares. Como este sistema de equações diferenciais não possui solução analítica, realizamos análise numérica para obter o comportamento dos campos de Higgs, de gauge e métricos em função da distância à corda cósmica. O modelo considerado apresenta dois campos bosônicos e um campo de gauge não-Abeliano. Como os dois setores bosônicos podem apresentar um acoplamento direto, investigamos a relevância deste acoplamento no sistema, especificamente na densidade linear de energia e no déficit de ângulo planar. Também analisamos o comportamento destas quantidades como função da escala de energia onde a simetria de gauge é espontaneamente quebrada. Ampliamos este estudo para as cordas cósmicas não-Abelianas no espaço-tempo de de Sitter e anti-de Sitter. Para isto, construímos um sistema de equações de campo considerando a presença da constante cosmológica. Utilizando a análise numérica, fornecemos o comportamento dos campos de Higgs, de gauge e dos campos métricos para valores específicos dos parâmetros físicos do modelo. Para o caso do espaço-tempo de de Sitter, salientamos o surgimento do horizonte cosmológico que, embora seja consequência da constante cosmológica, está fortemente relacionado ao acoplamento gravitacional. Para o espaço-tempo de anti-de Sitter, encontramos que o sistema não apresenta horizonte. Esta característica do sistema está relacionada às componentes (tt) e (zz) do tensor métrico, que divergem para grandes distâncias da corda cósmica.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2017-07-05T11:27:51Z No. of bitstreams: 1 rafaelleitefernandes.pdf: 295519 bytes, checksum: 990b7a9657e1e2be2738bb9b3dd7cf04 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-08T15:19:39Z (GMT) No. of bitstreams: 1 rafaelleitefernandes.pdf: 295519 bytes, checksum: 990b7a9657e1e2be2738bb9b3dd7cf04 (MD5) / Made available in DSpace on 2017-08-08T15:19:39Z (GMT). No. of bitstreams: 1 rafaelleitefernandes.pdf: 295519 bytes, checksum: 990b7a9657e1e2be2738bb9b3dd7cf04 (MD5) Previous issue date: 2013-02-27 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho vamos mostrar que o sistema chamado de “mundo brana” para representar o nosso Universo, introduzido por Randall-Sundrum (RS) no fim dos anos noventa, pode ser na verdade representado por branas curvas no espaço de de Sitter e Anti-de Sitter. Originalmente o sistema RS representaria um Universo com cinco dimensões onde o modelo padrão ficaria confinado em uma brana e os grávitons ficariam confinados na outra brana. Este sistema foi construído com uma métrica de Minkowski “torcida” com cinco dimensões onde os grávitons, responsáveis pelo campo gravitacional no modelo padrão, se deslocariam através da quinta dimensão, que por sua vez é infinita. E a ação padrão da relatividade geral, a ação de Einstein-Hilbert, foi a utilizada por RS. Neste trabalho de dissertação de mestrado vamos adotar uma ação modificada usada atualmente para explicar efeitos cosmológicos como a energia escura e a expansão do Universo por exemplo, ou seja, a ação com uma gravitação modificada chamada de f(R). Aqui vamos usar uma f(R) totalmente generalizada e suas consequências cosmológicas e viabilidade serão analisadas. Finalmente, vamos demonstrar que as partículas do modelo padrão estão confinadas nesta brana curva. Os resultados obtidos aqui generalizam totalmente outros resultados obtidos na literatura atual sobre mundo brana com branas grossas e são por isso, originais e serão submetidos à publicação. / In this work we will show that the so-called “brane world” framework introduced by Randall-Sundrum (RS), to represent our Universe, at the late nineties can be represented in fact by bent branes in de Sitter and Anti-de Sitter space with a generalized model for gravity. At the beginning, the RS scenario represent a Universe in five dimensions where the Standard Model is confined in one brane and the gravitons were confined in the another one. This model was build with a warped Minkowski metric with five dimensions where the gravitons, which are responsible by the gravitational field, are able to move through the fifth dimension, which is infinity. The standard general relativity action, namely, the Einstein-Hilbert action, was the one used by RS. In this Master dissertation we will adopt a modified action used at present to explain some cosmological effects like dark energy and Universe expansion, for example, i.e., we will use an action with a modified gravitation called f(R). However, here we will use a generalized f(R) and their cosmological consequences and viability will be analyzed. Finally, we will show that the particles of the Standard Model are confined at this bent brane. The results obtained here generalize altogether the others results obtained in the current literature concerning braneworlds with thick branes and are, consequently, new ones, which will be published elsewhere.

Ce travail étudie les variétés pseudo-riemanniennes compactes localement homogènes à travers le prisme des (G,X)-structures, introduites par Thurston dans son programme de géométrisation. Nous commençons par présenter la problématique générale et discutons notamment du rapport entre la complétude géodésique de ces variétés et une autre notion de complétude propre aux (G,X)-structures. Nous donnons également dans le chapitre 1 une nouvelle preuve d’un théorème de Bromberg et Medina qui classifie les métriques lorentziennes invariantes à gauche sur SL(2,R) dont le flot géodésique est complet. Conjecturalement, toute (G,X)-structure pseudo-riemannienne sur une variété compacte est complète. Nous prouvons ici que cela est vrai pour certaines géométries, sous l’hypothèse que la (G,X)-structure est a priori kleinienne. On en déduit que, pour ces géométries, la complétude est une condition fermée. Lorsque X est un groupe de Lie de rang 1 muni de sa métrique de Killing, ce résultat complète un théorème de Guéritaud–Guichard–Kassel–Wienhard selon lequel la complétude est une condition ouverte. Nous nous tournons ensuite vers l’étude des représentations d’un groupe de surface à valeurs dans les isométries d’une variété riemannienne M complète simplement connexe de courbure sectionnelle inférieure à -1. Étant donnée une telle représentation ρ, nous montrons que l’ensemble des représentations fuchsiennes j telles qu’il existe une application (j,ρ)-équivariante et contractante de H2 dans M est un ouvert non vide et contractile de l’espace de Teichmüller (sauf lorsque ρ est elle-même fuchsienne). Ce résultat nous permet de décrire l’espace des métriques lorentziennes de courbure constante -1 sur un fibré en cercle au-dessus d’une surface compacte. Nous montrons que cet espace possède un nombre fini de composantes connexes classifiées par un invariant que nous appelons longueur de la fibre. Nous prouvons également que le volume total de ces métriques ne dépend que de la topologie du fibré et de la longueur de la fibre. / In this work, we study closed locally homogeneous pseudo-Riemannian manifolds through the notion of (G,X)-structure, introduced by Thurston in his geometrization program. We start by presenting the general problem. In particular, we discuss the link between geodesical completeness of those manifolds and another notion of completeness specific to (G,X)-structures. In chapter 1, we also give a new proof of a theorem by Bromberg and Medina which classifies left invariant Lorentz metrics on SL(2,R) that are geodesically complete. Conjecturally, every pseudo-riemannian (G,X)-structure on a closed manifold is complete. Here we prove that it holds for certain geometries, provided that the (G,X )-structure is a priori Kleinian . This implies that, for such geometries, completeness is a closed condition. When X is a Lie group of rank 1 handled with its Killing metric, this result complements a theorem of Guéritaud–Guichard–Kassel–Wienhard, acording to which completeness is an open condition. We then turn to the study of representations of surface groups into the isometry group of a complete simply connected Riemannian manifold M of curvature less than or equal to -1. Given such a representation ρ, we prove that the set of Fuchsian representations j for which there exists a (j,ρ)-equivariant contracting map from H2 to M is a non-empty open contractible subset of the Teichmüller space (unless ρ itself is Fuchsian). This result allows us to describe the space of Lorentz metrics of constant curvature -1 on a circle bundle over a closed surface. We show that this space has finitely many connected components, classified by an invariant that we call the length of the fiber. We also prove that the total volume of those metrics only depends on the topology of the bundle and on the length of the fiber.

The conformal bootstrap method is a non-perturbative method that uses the symmetry in a conformal field theory to constrain and solve for the observables in the theory. We consider a conformal field theory with the symmetry group SU(N) and four general scalar fields as the only low dimensional operators. The four-point correlation function of a quartic interaction of four general scalar fields in a conformal field theory can be written as a sum over primary operators. In order to study the four-point correlator a large-N expansion is made, where N comes from the symmetry group SU(N). Using the conformal bootstrap method the anomalous dimension of the primary operators in the four-point correlator is calculated. Using the AdS/CFT correspondence the anomalous dimension of the primary operators is also calculated using Witten diagrams. / Konform fältteori är en kvantfältteori med konform symmetri. Konform symmetri är en symmetri som bevarar vinklar och lokalt ser ut som en kombination av en rotation och en förändring i skala. En metod för att beräkna de observerbara kvantiteterna i en konform fältteori är metoden "conformal boostrap". Denna metod går ut på att använda symmetrin i en konform fältteori för att begränsa och beräkna värdet på de observerbara kvantiteterna i teorin.En av de observerbar kvantiteterna i en fältteori är en korrelationsfunktion. Korrelationsfunktioner beskriver interaktionerna mellan partiklarna i en fältteori.  I detta arbete studerar vi en interaktion mellan fyra skalärfält genom att studera fyra-punkts korrelationsfunktionen för denna interaktion. Metoden vi använder är "conformal bootstrap" men vi testar också om AdS/CFT dualiteten håller för våra beräkningar. AdS/CFT dualiteten är en ekvivalens av två olika teorier, en strängteori i ett (d+1)-dimensionellt anti-de Sitter (AdS) rum och en konform fältteori (CFT) i den d-dimensionella gränsen av anti-de Sitter rummet. Enligt denna dualitet kan en observerbar kvantitet beräknas från båda dessa två teorier och ge samma resultat. Teorin vi studerar har symmetrigrupp SU(N) och vi arbetar i dimension två. Vi arbetar också med att N, matrisrangen i teorin, är stort då detta är den gräns där AdS/CFT dualiteten gäller. Enligt konform fältteori så kan en fyra-punkts korrelationsfunktion av fyra skalärer beskrivas som en summa över vad som kallas primära fält. Genom att använda "conformal bootstrap" metoden beräknas den anormala dimensionen, vilket är en korrektion av första icke-triviala ordning till dimensionen, av dessa primära fält. Samma kvantitet beräknas också från strängteorisidan av AdS/CFT dualiteten genom användandet av så kallade Witten diagram. Resultatet från båda sidor av dualiteten visas stämma överens.

I construct anti-de Sitter boson stars in Einstein-Gauss-Bonnet gravity coupled to a (D-1)/(2)-tuplet of complex massless scalar field both perturbativelyand numerically in D=5,7,9,11 dimensions. Due to the choice of scalar fields, these solutions possess just a single helical Killing symmetry. For each choice of the Gauss-Bonnet parameter &alpha;&#8800;&alpha;_cr, the central energy density at the center of the boson star, q_0 completely characterizes the one parameter family of solutions. These solutions obey the first law of thermodynamics, in the case of the numerics, to within 1 part in 10^6. I describe the dependence of the boson star mass, angular momentum and angular velocity on &alpha; and on the dimensionality. For &alpha;<&alpha;_cr and D>5, these quantities exhibit damped oscillations about finite central values and the central energy density tends to infinity. The Kretschmann invariant at the center of the boson star diverges in the limit of diverging central energy. This contrasts the D=5 case, where the Kretschmann invariant diverges at a finite value of the central energy density. Solutions where &alpha;<&alpha;_cr, correspond to negative mass boson stars, and the for all dimensions the boson star mass and angular momentum decrease exponentially as the central energy density tends toward infinity with the Kretschmann invariant diverging only when in the limit the central energy density diverges. I also briefly discuss the difficulties of numerically obtaining single Killing vector hairy black hole solutions and present the explicit boundary conditions for both Einstein gravity and Einstein-Gauss-Bonnet gravity.

Comme introduction, nous présentons la formulation originale de la correspondance AdS/CFT, entre la théorie de Yang-Mills supersymétrique N = 4 avec groupe de jauge SU(N) et la théorie des supercordes de type IIB sur l'espace AdS5 x S5. Dans une première partie, nous montrons comment les ingrédients de la correspondance AdS/CFT peuvent être appliqués de manière phénoménologique à l'étude des systèmes de fermions fortement corrélés et présentons deux modèles fondamentaux, l'étoile à électrons et le supraconducteur holographique. Nous construisons un modèle holographique pour l'étude des systèmes de Bose-Fermi à densité finie et montrons que la présence simultanée de degrés de liberté bosoniques et fermioniques est favorisée à température nulle. En résolvant l'équation du mouvement d'un spineur test sur ces solutions, nous montrons que le système admet un grand nombre de surfaces de Fermi de type électron et/ou trou et un condensat scalaire chargé. Dans une seconde partie, nous nous intéressons à l'étude des solutions de trous noirs BPS asymptotiquement AdS4 dans la théorie de supergravité jaugée N = 2 en 4 dimensions. En utilisant les transformations de dualité dans un modèle STU simple, nous trouvons de nouvelles solutions de trous noirs BPS statiques et en rotation. / As an introduction, we present the original formulation of the AdS/CFT correspondence, between N = 4 Super Yang-Mills theory with gauge group SU(N) and type IIB string theory on AdS5 x S5. In a first part, we show how the ingredients of the AdS/CFT correspondence can be applied in a phenomenological way to study strongly correlated systems of fermions and present two fundamental models, the electron star and the holographic superconductor. We construct a holographic model for the study of Bose-Fermi systems at finite density and show that the simultaneous presence of bosonic and fermionic degrees of freedom is favoured at zero temperature. By solving the field equation of a probe spinor field in these solutions, we show that the system admits a large number of electron-like and/or hole-like Fermi surfaces and a charged scalar condensate. In a second part, we study asymptotically-AdS4 BPS black hole solutions in the N = 2 gauged supergravity theory. Using the duality transformations in a simple STU model, we find new static and rotating BPS black hole solutions.

In this work we investigate an exact solution of Einstein's equations which is described by the Pleba'nski-Demia'nski metric. This metric represents type D space-times and contains seven free parameters, including electric and magnetic charges and a cosmological constant. We study geometrical and phy- sical properties of these space-times in the case when repeated principal null congruences have zero expansion. Therefore, first we study de Sitter universe and anti-de Sitter universe in the Pleba'nski-Demia'nski coordinates, and we care- fully analyze the corresponding parametrizations of (anti-)de Sitter hyperboloid in five-dimensional flat space-time, unknown so far, we draw the respective con- formal diagrams, and we find transformations to various known forms. After that, we investigate the more general case of the B metrics with a cosmological con- stant, and we do a basic analysis of its geometrical properties. We summarize the article by Gott from 1974, where he interprets the BI metric as a part of space-time with a tachyon singularity, and we generalize his results for the case of non-zero cosmological constant. Finally, we analyze even more general cases of the Pleba'nski-Demia'nski metric with more non-zero parameters. In particular, we study the electromagnetic field in the case of non-zero...