In this thesis we use the holographic gauge/gravity duality to study two different aspects of strongly coupled non-Abelian plasmas. In the first topic we study the effects of strong (Abelian) magnetic fields on the transport coefficients of a strongly coupled non-Abelian plasma. Due to the spatial anisotropy created by the magnetic field, the most general viscosity tensor of a magnetized plasma has 5 shear viscosity coefficients and 2 bulk viscosities. We use the holographic correspondence for a strongly coupled N=4 Supersymmetric Yang-Mills (SYM) plasma to evaluate the shear viscosity perpendicular to the magnetic field and the shear viscosity parallel to the field. In the presence of a magnetic field, the shear viscosity perpendicular to the field saturates the Kovtun-Son-Starinets viscosity bound while in the direction parallel to the field the bound is violated. The second topic investigated in this thesis is motivated by the study of the near equilibrium behavior of strongly interacting non-Abelian plasmas that display a critical point in their phase diagram. We focus on the spectra of non-hydrodynamic quasinormal modes of a strongly coupled N=4 SYM plasma in the presence of a chemical potential, which displays a critical point in equilibrium. Except close to the critical point, we observe that by increasing the chemical potential one generally increases the damping rate of the quasinormal modes, which leads to a reduction of the characteristic equilibration times in the dual strongly coupled plasma. However, as one approaches the critical point the typical equilibration time increases though its derivative with respect to the chemical potential diverges with an exponent equal to -1/2. We also find a purely imaginary non-hydrodynamical mode in the vector diffusion channel at nonzero chemical potential which dictates the equilibration time in this channel near the critical point. / Nessa tese usamos a dualidade holográfica calibre/gravidade para estudar dois aspectos diferentes de plasmas não-Abelianos fortemente acoplados. No primeiro tópico estudamos os efeitos de campos magnéticos (Abelianos) intensos sobre o coeficientes de transporte de um plasma não-Abeliano fortemente acoplado. Devido à anisotropia espacial criada pelo campo magnético, o tensor de viscosidade mais geral de um plasma magnetizado deve possuir 5 coeficientes de viscosidade de cisalhamento e 2 de viscosidade volumétrica. Usamos a correspondência holográfica para um plasma N=4 Supersimétrico de Yang-Mills (SYM) fortemente acoplado para calcular a viscosidade de cisalhamento perpendicular ao campo magnético e a viscosidade de cisalhamento paralela ao campo. Na presença do campo magnético, a viscosidade de cisalhamento perpendicular ao campo satura o limite viscoso de Kovtun-Son-Starinets enquanto que na direção paralela ao campo o limite é violado. O segundo tópico investigado nessa tese é motivado pelo estudo do comportamento próximo ao equilíbrio de plasmas não-Abelianos fortemente interagentes que exibem um ponto crítico em seus diagramas de fase. Focamos no espectro dos modos quasinormais não-hidrodinâmicos de um plasma N=4 SYM fortemente acoplado na presença de um potencial químico, que exibe um ponto crítico no equilíbrio. Exceto próximo ao ponto crítico, observamos que ao aumentar o potencial químico geralmente se intensifica a taxa de amortecimento dos modos quasinormais, que levam à redução dos tempos de equilibração característicos do plasma dual fortemente acoplado. Entretanto, aproximando-se do ponto crítico o tempo de equilibração típico aumenta embora sua derivada em relação ao potencial químico diverge com um expoente igual à -1/2. Encontramos também um modo não-hidrodinâmico puramente imaginário no canal de difusão vetorial com potencial químico não-nulo que dita o tempo de equilibração neste canal próximo do ponto crítico.

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.

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.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Quasinormal modes of plane-symmetric anti-de Sitter (AdS) black holes in d spacetime dimensions are investigated. Following the gauge invariant prescription developed by Kodama, Ishibashi and Seto (2000), fundamental equations for gravitational perturbation in such a background are constructed. Within such a prescription, metric perturbations naturally split into three disjoint classes. Namely, tensor, vector and scalar perturbations. However, different gauge invariant quantities are chosen in the present work, because they are more suited to the particular boundary conditions usually imposed to find quasinormal modes in AdS spacetimes than those used by Kodama, Ishibashi and Seto. In particular, the quantities used here present also the so called hydrodynamic modes, i. e., shear modes for vector perturbations and sound wave modes for the scalar ones, what is not found using the former quantities. It is also shown that there is just one shear mode, which does not depend upon the number of spacetime dimensions (d). Moreover, it is also found a general expression for the sound wave modes in terms of the number of the parameter d for scalar perturbations, and that there is no such a hydrodynamic mode for the tensor sector. Horowitz-Hubeny power series method is used in numerical analysis to find the dispersion relations for the first few quasinormal modes, and also for the hydrodynamic modes. This analysis is performed for five and six spacetime dimensions in the case of tensor perturbations, and for four, five and six dimensions in the cases of vector and scalar perturbations. The dispersion relations of regular modes present the same general behavior for all kinds of perturbations, Re(w) → q and Im(w) → 0 in the limit q → ∞, where w and q are the normalized frequency and the normalized wave number, respectively. / Investiga-se os modos quase-normais gravitacionais de buracos negros plano-simétricos anti-de Sitter em d dimensões, cuja geometria das seções espaciais é plana e cuja topologia pode ser plana, cilíndrica ou toroidal. Deduz-se equações fundamentais de perturbação gravitacional para este background, seguindo o formalismo invariante de gauge desenvolvido por Kodama, Ishibashi e Seto (2000), segundo o qual as perturbações métricas são naturalmente separadas em três setores ortogonais: tensorial, vetorial e escalar. Entretanto, são escolhidas diferentes quantidades invariantes de gauge tais que sob condições de contorno apropriadas fornecem os modos quase-normais hidrodinâmicos do buraco negro em questão. Particularmente, no limite hidrodinâmico, os modos de cisalhamento nas perturbações gravitacionais vetoriais e modos de onda sonora nas perturbações escalares são encontrados explicitamente. Mostra-se que o modo de cisalhamento é único e independe do número de dimensões, apresenta-se uma expressão para o modo de onda sonora válida para qualquer dimensão e verifica-se que as perturbações gravitacionais tensoriais não apresentam modos hidrodinâmicos. Utiliza-se o método de Horowitz-Hubeny para calcular numericamente os primeiros modos quase-normais comuns para cada setor de perturbação e apresentam-se as respectivas relações de dispersão Re(w) × q e Im(w)×q, onde w são as freqüências quase-normais e q é o número de onda normalizados. Também obtêm-se numericamente os modos hidrodinâmicos e suas relações de dispersão. Os modos quase-normais das perturbações tensoriais são calculados para buracos negros plano-simétricos anti-de Sitter em cinco e seis dimensões, e os modos quase-normais das perturbações vetoriais e escalares são calculados para buracos negros em quatro, cinco e seis dimensões. Observa-se que as relações de dispersão apresentam um comportamento geral onde Re(w) → q e Im(w) → 0 conforme q → ∞ independentemente do tipo de perturbação, número de dimensões e do modo quase-normal analisado.

Classical theory cannot provide a satisfying scenario for a unitary thermodynamic evolution of black holes. To preserve information one requires quantum mechanical effects on scales reaching beyond the traditional horizon radius. Therefore, common to many of the theories attempting to resolve the paradox is the existence of exotic horizon structures. The recent advent of gravitational wave astronomy provides a possible means for detecting the existence of such structures through gravitational wave emission in the ringdown phase of binary black hole mergers. Such emission is described by quasinormal modes (QNMs) in which the gravitational waves originates outside the black hole, in the vicinity of the photon spheres. Requiring reflective properties of the horizon structure results in the existence of gravitational echoes that may be detected by facilities such as LIGO etc.. This thesis studies geodesic motion of such echoes in the equatorial plane of a rotating black hole. Depending on the extent of the horizon structure, and the particular mode of emission, one can expect different timescales for the echoes. For a horizon structure extending <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CLambda%20r%20=" /> <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?10%5E%7B-12%7D" /> <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?M" /> outside the traditional horizon of a  <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?M%20=%2022.6%20M_%7B%5Codot%7D" />, <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?a%20=%200.74%20M" /> black hole one would ideally find echoes appearing as integer multiples of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20t_%7Becho%7D" /><img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?=%200.0204%20s" /> after the primary signal. The time delay is expected to increase by at least an order of magnitude if one lets <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20r%20%5Csim%2010%5E%7B-80%7D%20M" />. The expected echo timescales for gravitational waves emitted from any point around the black hole, in arbitrary modes, is an interesting further study.

Dumb holes (also known as acoustic black holes) are fluid flows which include an "acoustic horizon:" a surface, analogous to a gravitational horizon, beyond which sound may pass but never classically return. Soundwaves in these flows will therefore experience "effective geometries" which are identical to black hole spacetimes up to a conformal factor. By adjusting the parameters of the fluid flow, it is possible to create an effective geometry which is conformal to the Anti-de Sitter black hole spacetime- a geometry which has recieved a great deal of attention in recent years due to its conjectured holographic duality to Conformal Field Theories. While we would not expect an acoustic analogue of the AdS-CFT correspondence to exist, this dumb hole provides a means, at least in principle, of experimentally testing the theoretical properties of the AdS spacetime. In particular, I have calculated the quasinormal mode spectrum of this acoustic geometry. / Graduate / 0986 / 0753 / jpbabb@yahoo.ca

The idea of holography [1, 2] finds a concrete realization in form of the AdS/CFT correspondence [3, 4]. This duality relates a field theory with conformal symmetries to quantum gravity living in one higher dimension. In this thesis we study aspects of black hole quasinormal modes, higher spin theories and entanglement entropy in the context of this duality. In almost all cases we have been able to subject the duality to some precision tests. Quasinormal modes encode the spectrum of black holes and the time-scale of pertur- bations therein [5]. From the dual CFT viewpoint they are the poles of retarded Green's function (or peaks in the spectral function) [6]. Quasinormal modes were previously studied for scalar, gauge field and fermion fluctuations [7]. We solve for these quasinormal modes of higher spin (s _ 2) fields in the background of the BTZ black hole [8, 9]. We obtain an exact solution for a field of arbitrary spin s (integer or half-integer) in the BTZ background. This implies that the BTZ is perhaps the only known black hole background where such an analysis can be done analytically for all bosonic and fermionic fields. The quasinormal modes are shown to match precisely with the poles of the corresponding Green's function in the CFT living on the boundary. Furthermore, we show that one-loop determinants of higher spin fields can also be written as a product form [10] in terms of these quasinormal modes and this agrees with the same obtained by integrating the heat-kernel [11]. We then turn our attention to dualities relating higher-spin gravity to CFTs with W algebra symmetries. Since higher spin gravity does go beyond diffeomorphism invariance, one needs re_ned notions of the usual concepts in differential geometry. For example, in general relativity black holes are defined by the presence of the horizon. However, higher spin gravity has an enlarged group of symmetries of which the diffeomorphisms form a subgroup. The appropriate way of thinking of solutions in higher spin gravity is via characterizations which are gauge invariant [12, 13]. We study classical solutions embedded in N = 2 higher spin supergravity. We obtain a general gauge-invariant condition { in terms of the odd roots of the superalgebra and the eigenvalues of the holonomy matrix of the background { for the existence of a Killing spinor such that these solutions are supersymmetric [14]. We also study black holes in higher spin supergravity and show that the partition function of these black holes match exactly with that obtained from a CFT with the same asymptotic symmetry algebra [15]. This involved studying the asymptotic symmetries of the black hole and thereby developing the holographic dictionary for the bulk charges and chemical potentials with the corresponding quantities of the CFT. We finally investigate entanglement entropy in the AdS3/CFT2 context. Entanglement entropy is an useful non-local probe in QFT and many-body physics [16]. We analytically evaluate the entanglement entropy of the free boson CFT on a circle at finite temperature (i.e. on a torus) [17]. This is one of the simplest and well-studied CFTs. The entanglement entropy is calculated via the replica trick using correlation functions of bosonic twist operators on the torus [18]. We have then set up a systematic high temperature expansion of the Renyi entropies and determined their finite size corrections. These _nite size corrections both for the free boson CFT and the free fermion CFT were then compared with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces (replica geometry) as its boundary [19]. One-loop corrections in these geometries are entirely determined by the spectrum of the excitations present in the bulk. It is shown that the leading _nite size corrections obtained by evaluating the one-loop determinants on these handlebody geometries exactly match with those from the free fermion/boson CFTs. This provides a test for holographic methods to calculate one-loop corrections to entanglement entropy. We also study conformal field theories in 1+1 dimensions with W-algebra symmetries at _nite temperature and deformed by a chemical potential (_) for a higher spin current. Using OPEs and uniformization techniques, we show that the order _2 correction to the Renyi and entanglement entropies (EE) of a single interval in the deformed theory is universal [20]. This universal feature is also supported by explicit computations for the free fermion and free boson CFTs { for which the EE was calculated by using the replica trick in conformal perturbation theory by evaluating correlators of twist fields with higher spin operators [21]. Furthermore, this serves as a verification of the holographic EE proposal constructed from Wilson lines in higher spin gravity [22, 23]. We also examine relative entropy [24] in the context of higher-spin holography [25]. Relative entropy is a measure of distinguishability between two quantum states. We confirm the expected short-distance behaviour of relative entropy from holography. This is done by showing that the difference in the modular Hamiltonian between a high-temperature state and the vacuum matches with the difference in the entanglement entropy in the short-subsystem regime.