L’objet de cette thèse est l’étude de la correspondance fluide/gravité, réalisation macroscopique de la dualité AdS/CFT, à la limite où la constante cosmologique tend vers zéro (limite plate). La jauge de Fefferman-Graham, habituellement utilisée dans le dictionnaire holographique, est singulière à la limite plate. Ici, en passant par la formulation hydrodynamique de la théorie dubord, nous construisons une jauge, appelée jauge du développement en série dérivatif, où cette limite est bien définie. Sur la géométrie du bord, elle correspond en fait à faire tendre vers zéro la vitesse de la lumière, situation connue comme limite carrollienne. Un fluide relativiste admet une telle lim-ite, qui donne lieu à l’hydrodynamique carrollienne, étudiée ici en dimension arbitraire, parallèlement à son homologue galiléen. Ensuite, nous montrons spécifiquement en dimensions 4 et 3 du bulk qu’il est possible de construire des solutions asymptotiquement plates des équations d’Einstein partant de systèmes hydrodynamiques conformes carrolliens du bord, qui est ici l’hypersurface degenre lumière à l’infini. En 4 dimensions nous introduisons des conditions d’intégrabilité permettant de resommer la série dérivative sous formefermée. En 3 dimensions toute configuration fluide du bord aboutit à une solution exacte des équations d’Einstein. Les solutions de Bañados sont un sous-ensemble des solutions obtenues et identifiées au moyen de leurs charges de surface. Nous accordons une attention particulière au rôle du repère hydrodynamique, trop souvent ignoré en holographie. Pour terminer, nous nous concentrons sur la formulation de la AdS/CFT dans laquelle la symétrie de Weyl est explicite. Quoique cette symétrie soit un ingrédient incontournable de la correspondance fluide/gravité, elle n’est pas codée dans la formulation habituelle de l’holographie. Nous introduisons une nouvelle jauge et analysonsses conséquences. / In this thesis we discuss the limit of vanishing cosmological constant (flat limit) of the fluid/gravity correspondence, which is a macroscopic realization of the AdS/CFT. The holographic dictionary is usually implemented in a gauge(Fefferman-Graham), which does not admit a flat limit. In the hydrodynamic formulation of the boundary theory, we introduce a gauge, dubbed derivative expansion, where such a limit turns out to be smooth. In the boundary we show that this corresponds to a Carrollian limit, i.e. a limit where the speed of light vanishes. We present Carrollian hydrodynamics, together with its dual Galilean counterpart. Then, for 4 and 3 bulk dimensions, we exhibit a resummed line element, which provides an asymptotically flat bulk solution of Einsteinequations starting only from boundary (i.e. null infinity) conformal Carrollian hydrodynamic data. In 4 dimensions we exploit specific integrability conditions, which restrict the achievable class of solutions in the bulk. In 3 dimensions every boundary fluid configuration leads to an exact solution of Einstein’s equations. Bañados solutions are a subset of the solutions reached in this way. They are rigorously identified with their surface charges and the corresponding algebra. We emphasize the choice of hydrodynamic frame, often sidesteppedin holography. Finally, we focus on the formulation of AdS/CFT to encompass Weyl symmetry. This symmetry is a key ingredient of fluid/gravity but it is not naturally encoded in the usual formulation of holography. We introduce an appropriate gauge for realizing it, and analyze its far-reaching consequences.

Les trous noirs sont produits par effondrement gravitationnel d'étoiles supermassives et contiennent en leur centre une singularité de l'espace-temps habillée d'un horizon auquel rien ne peut s'échapper. Ils se situent à la frontière théorique commune entre la Relativité Générale et la Mécanique Quantique, ce qui en fait le principal laboratoire théorique et expérimental pour tester les théories quantiques de la gravité comme la Théorie des Cordes. L'entropie d'un trou noir est énorme, de l'ordre de sa masse au carré. Comme tout objet entropique, une description microscopique en termes de dégénérescence d'états devrait exister. De plus, le trou noir s'évapore par rayonnement d'Hawking et l'information à l'intérieur semble perdue, ce qui compromet la principe d'unitarité, pierre angulaire de la Mécanique Quantique. Par conséquent, la Théorie des Cordes doit fournir les degrés de liberté nécessaires pour décrire la nature de micro-état de trous noirs, elle doit également trouver un mécanisme résolvant la singularité et le paradoxe de la perte d'information. Cette thèse porte sur la physique des trous noirs à travers le "fuzzball proposal" et le "microstate geometry program". La majeure partie de la discussion se déroulera dans la limite de basse énergie de la Théorie des Cordes, c'est-à-dire en Supergravité. Le ``proposal" stipule qu'il existe "eS" solutions non singulières sans horizon qui ressemblent à un trou noir à large distance mais qui diffèrent à proximité de l'horizon. Sur la base de cette affirmation, la solution de trou noir classique correspond à la description statistique d'un système de solutions qui ont la même géométrie que le trou noir à l'extérieur de l'horizon, mais qui se terminent par des géométries régulières, dites "fuzzy". La proposition soulève plusieurs questions : Comment la singularité est-elle résolue ? De telles géométries peuvent-elles être construites en Supergravité ? Comment l'information s'échappe-t-elle de l'ensemble des micro-états ? La thèse est décomposée en trois parties. La première partie présente les bases et donne un aperçu du "microstate geometry program". La deuxième partie regroupe cinq travaux qui se consacrent à construire de larges familles de micro-états de trous noirs supersymétriques ou non supersymétriques. La dernière partie passe en revue deux travaux. L'un d'eux étudie le processus de diffusion dans les micro-états. Cela permet d'élucider comment le principe d'unicité est restaurée et comment l'information s'échappe des micro-états. La seconde traite du rôle des micro-états dans le contexte de la correspondance AdS2/CFT1 et donne l'ébauche d'une preuve pour le "fuzzball proposal". / Black holes are produced by gravitational collapse of supermassive stars and consist of a spacetime singularity dressed by a horizon from which nothing can escape. They lie at the common theoretical border between General Relativity and Quantum Mechanics, making them the main theoretical and experimental laboratory for testing quantum theories of gravity as String theory. The entropy of a black hole is huge, of the order of its mass squared. As any entropic object, a microscopic description in terms of large degeneracy of states should exist. Moreover, black hole evaporates through thermal Hawking's radiation and the information in the interior seems lost, that compromises the unitary principle, a cornerstone of Quantum Mechanics. Therefore, String Theory must provide the degrees of freedom necessary to describe the microstate nature of black holes, it must also find a mechanism resolving the singularity and the information loss paradox. This thesis addresses black-hole physics through the lens of the fuzzball proposal and the microstate geometry program. The major part of the discussion will be conducted in the low-energy limit of String Theory, that is in Supergravity. The proposal states that there exist "eS" horizonless non-singular solutions that resemble a black hole at large distance but differ in the vicinity of the horizon. Based on this statement, the classical black-hole solution corresponds to the average description of a system of solutions which match the black-hole geometry outside the horizon but cap off as ``fuzzy" smooth geometries in the infrared. The proposal leads to several questions: How is the singularity resolved? Can "eS" such geometries be built in Supergravity? How does the information escape from the ensemble of microstates?The thesis is decomposed in three parts. The first part introduces the basic materials and gives a review of the microstate geometry program. The second part gathers five works that all consist in constructing large classes of smooth horizonless microstate geometries of supersymmetric or non-supersymmetric black holes. The last part review two works. One is investigating the scattering process in microstate geometries. This helps to elucidate how unitarity is restored and how information escapes from black-hole backgrounds. The second one addresses the role of microstate geometries in the context of the AdS2/CFT1 correspondence and gives a beginning of proof for the fuzzball proposal.

In this thesis we study various aspects of integrable methods in AdS3/CFT2 holog- raphy. These techniques come from exploiting special form of gauge compatible with asymptotic boundary conditions on the bulk fields in Chern Simons formulation of 3d gravity and higher spin theories. The integrable systems emerging are so called Toda field theories. The rigid structure of these theories allows us to learn more about certain gravitational solutions - multi centered solutions. One of the most interesting applications of the formalism developed is in the problem of black hole deconstruction and information paradox where we can read of the information about the temperature from the Toda field theory charges and. Aside of the gravitational applications we also study a vast generalization of the WZW to Toda field theory reduction and its connection to the Closed Toda systems. 1

This thesis explores the expansive world of General Relativity, and its role to play in modern cosmology and quantum field theory. We begin with a pedagogical approach to relativity, in particular, highlighting upon the ambiguity that arises with the conventions used in different textbooks. A brief introduction to tensor calculus has also been provided in the appendix. The preliminary chapters are also complimented with examples of numerical relativity via simulation. We then move on to discuss examples of non-linear systems, and their exact solutions. Such systems will be analogous to those we shall encounter later, upon considering scalar field theories as a means of modelling dark energy. We shall introduce the axion as our highly motivated dark matter candidate, since this will ultimately determine the behaviour of the scalar field. Coupled to a scaling factor across the spatial domain, it is found that this scalar field will ultimately determine the evolution of our universe. The key result of this thesis has been the possibility to screen both the cosmological constant, and flatness of the universe, to within observable parameters. These results will be explicitly derived from first principles. Also included is a tentative approach to holographic theory, in which strongly correlated systems may be modelled within the asymptotic domain of Anti-de Sitter (AdS) space. Ultimately, our aspirations are to bridge the gap with condensed matter theory, in particular with the publications included within the latter appendices. These publications discuss graphene as a revolutionary new material, for inclusion in both transistor-based and optoelectronic devices.

The formulation of rigid supersymmetric field theories on curved space leads to a number of results on their strongly-interacting regime, crucial from both the mathematical and physical point of view, starting from Witten's topological twist of four-dimensional Yang-Mills theory. At the same time, strongly-coupled field theories may also be studied holographically via the AdS/CFT correspondence. The aim of this thesis is to study aspects of the holographic dictionary for supersymmetric theories on curved manifolds. A key aspect of the correspondence is the renormalization of gravity observables, which is realized via holographic renormalization. If the dual boundary field theory is supersymmetric, it is natural to ask whether this scheme is compatible with the rigid supersymmetry at the curved boundary. The latter requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. We may then formulate a precise check of the holographic dictionary by asking whether the dual holographic observables are similarly invariant, as the free energy of the gauge theory is identified with the holographically renormalized supergravity action. In the first part of the thesis, we consider this question in N = 4 gauged supergravity in four and five dimensions for the holographic dual to the topological twists of N = 4 gauge theories on Riemannian three-manifolds and N = 2 gauge theories on Riemannian four-manifolds. We show that the renormalized on-shell action is independent of the metric on the boundary four-manifold, as required for a topological theory. We then go further, analyzing the geometry of supersymmetric bulk solutions. This allows us to show that the gravitational free energy of any smooth filling vanishes in both AdS₄/CFT₃ and AdS₅/CFT₄. In the second part of the thesis, we study the same question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results for the dependence of the partition function on the background. Surprisingly, in five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges. We also briefly comment on the relation between these terms and boundary supercurrent anomalies.

In this Ph.D. thesis, we construct and study a number of new type IIB supergravity backgrounds that realize various flavored, finite temperature, and non-supersymmetric deformations of the resolved and deformed conifold geometries. We make heavy use of a U-duality solution generating procedure that allows us to begin with a modification of a family of solutions describing the backreaction of D5 branes wrapped on the S^2 of the resolved conifold, and generate new backgrounds related to the Klebanov-Strassler background. We first construct finite temperature backgrounds which describe a configuration of N_c D5 branes wrapped on the S^2 of the resolved conifold, in the presence of N_f flavor brane sources and their backreaction i.e. N_f/N_c ~ 1. In these solutions the dilaton does not blow up at infinity but stabilizes to a finite value. The U-duality procedure is then applied to these solutions to generate new ones with D5 and D3 charge. The resulting backgrounds are a non-extremal deformation of the resolved deformed conifold with D3 and D5 sources. It is tempting to interpret these solutions as gravity duals of finite temperature field theories exhibiting phenomena such as Seiberg dualities, Higgsing and confinement. However, a first necessary step in this direction is to investigate their stability. We study the specific heat of these new flavored backgrounds and find that they are thermodynamically unstable. Our results on the stability also apply to other non-extremal backgrounds with Klebanov-Strassler asymptotics found in the literature. In the second half of this thesis, we apply the U-duality procedure to generate another class of solutions which are zero temperature, non-supersymmetric deformations of the baryonic branch of Klebanov-Strassler. We interpret these in the dual field theory by the addition of a small gaugino mass. Using a combination of numerical and analytical methods, we construct the backgrounds explicitly, and calculate various observables of the field theory. / text

The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. We propose propose two possible approaches to establish this correspondence: perturbative expansion for shear modes and large mean curvature expansion for algebraically special metrics. / Physics

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No. of bitstreams: 1 ramponi_tc_me_rcla.pdf: 1200399 bytes, checksum: d003d0863c0473e1dd98e7a7ea4aa402 (MD5) Previous issue date: 2018-09-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo desse trabalho concentra-se em estudar uma nova metodologia para resolução de problemas em matéria condensada, nos quais as partículas estão fortemente acopladas, não permitindo um tratamento perturbativo padrão. Esse método, originário da dualidade AdS/CFT (Anti-de Sitter/Conformal Field Theory), está sendo conhecido na comunidade de matéria condensada como Dualidade Holográfica. Como aplicação desta teoria, o comportamento de supercondutores foi escolhido. A metodologia da dualidade holográfica utiliza uma teoria de campos em um espaço-tempo curvo. Partindo da ação associada é possível obter as equações de movimento das partículas envolvidas. A seguir foi empregado o uso do software Mathematica-Wolfram, para a resolução das Equações Diferenciais através do Método de Frobenius. Os resultados obtidos expressam que os valores esperados de operadores, as chamadas funções de correlação, são bem similares à curva de intervalo de energia previsto pela teoria BCS em função da temperatura. Também infere-se a partir da fórmula de Kubo, que os resultados numéricos da condutividade elétrica, claramente indicam uma condutividade infinita abaixo de uma determinada temperatura crítica Tc, resultando em um supercondutor. / The objective of this work is to study a new methodology for solving problems in condensed matter, in which the particles are strongly coupled, not allowing a standard perturbative treatment. This method, originating from the AdS / CFT (Anti-Sitter / Conformal Field Theory) duality, is being known in the condensed matter community as Holographic Duality. As an application of this theory, the behavior of superconductors was chosen. The holographic duality methodology uses a field theory in a curved space-time. From the associated action it is possible to obtain the equations of motion of the particles involved. Next, the use of the Mathematica-Wolfram software was used to solve the Differential Equations by the Frobenius Method. The obtained results express that the expected values of operators, so-called correlation functions, are very similar to the energy interval curve predicted by the BCS theory as a function of temperature. It is also inferred from the Kubo formula that the numerical results of electrical conductivity clearly indicate an infinite conductivity below a given critical temperature Tc, resulting in a superconductor. / CAPES: 001

In this thesis we consider various applications the gauge/gravity duality to study transport in strongly coupled systems. The main content is organized in three parts. In the first part we investigate the interrelation between dimensionality and strength of interactions. It is known that the dynamics of systems in Condensed Matter and General Relativity simplify for high dimensionality. Therefore, in this limit of large dimensionality, analytic results are usually possible. We study the dependence of the conductivity and the entanglement entropy on the space-time dimensionality in two different models of holographic superconductors: one dual to a quantum critical point with spontaneous symmetry breaking, and the other modelled by a charged scalar that condenses at a sufficiently low temperature in the presence of a Maxwell field. In the large dimensionality limit we obtain explicit analytical results for the conductivity at zero temperature and the entanglement entropy. Our results suggest that, as dimensionality increases, the condensate interactions become weaker. In the second part we first investigate the Drude weight and the related Mazur-Suzuki (MS) bound in a broad variety of strongly coupled field theories with a gravity dual at nonzero temperature and chemical potential. We show that the MS bound, which in the context of Condensed Matter provides information on the integrability of the theory, is saturated in Einstein-Maxwell-dilaton (EMd) and R-charged backgrounds. We then explore EMd theories with U(1) spontaneous symmetry breaking, and gravity duals of non-relativistic field theories, in which the MS bound is not saturated. Finally, we study the effect of a weak breaking of translational symmetry and we show that the MS bound sets a lower bound on the DC conductivity for a given scattering time. In the last part, we study asymptotically anti de Sitter Brans-Dicke (BD) backgrounds as effective models of metals with a varying coupling constant. We show that, for translational invariant backgrounds, the zero-frequency conductivity (dc conductivity) deviates from the universal result of EMd models. Once translational symmetry is broken, the shear viscosity to entropy ratio is always lower than the Kovtun-Son-Starinets bound, in line with other gravity backgrounds with momentum relaxation. In the BD models studied, we observed insulating like features in the dc conductivity. However, the module and argument of the optical conductivity at intermediate frequencies are not consistent with cuprates experimental results, even assuming several channel of momentum relaxation. We have also included the research carried out in the first year of the PhD as appendices. The topics studied in these appendices lie outside the main framework of this thesis.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22996号 / 理博第4673号 / 新制||理||1670(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高柳 匡, 教授 杉本 茂樹, 教授 田中 貴浩 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM