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.

Ätstörningar är allvarliga sjukdomar som medför stort lidande för patienter och deras närstående. De rekommenderadebehandlingsmetoderna kan hjälpa vissa patienter men det behövs effektivare behandlingsmetoder. Det finns teoretiskt stöd och ännu begränsat empiriskt stöd för att compassionfokuserad terapi (CFT) kan vara hjälpsam för patienter med ätstörningar. I föreliggande studie var syftet att utvärdera CFT i grupp vad gäller metodens genomförbarhet, acceptabilitet och preliminära effektivitet för patienter med ätstörningar som behandlas i dagvård. En åttasessioners manualbaserad CFT-grupp som tillägg till ätstörningsdagvård utvärderades enligt en single-group studiedesign (n=8). CFT-gruppen visade god genomförbarhet och acceptabilitet. Patienter förbättrades med måttliga till stora effektstorlekar vad gäller ätstörningssymptom, vikt, självkritik och självuppmuntran. Dock uppnådde inget effektmått statistisk signifikans. Studiens resultat tyder på att CFT i grupp som tillägg till ätstörningsdagvård kan vara en genomförbar och acceptabel behandling som möjligen kan bidra till tillfriskande av patienter med ätstörningar. / Eating disorders are serious illnesses that cause great suffering for patients and their caregivers. The recommended treatment methods help some patients, but more effective treatment methods are needed. There is theoretical support and still limited empirical support that compassion-focused therapy (CFT) may be helpful for patients with eating disorders. The aim of the present study was to evaluate the feasibility, acceptability and preliminary effectiveness of group CFT for patients with eating disorders who receive day care treatment. An eight-session manual-based CFT group was evaluated as an adjunct to day patient program for eating disorders according to a single-group design (n=8). The CFT group demonstrated good feasibility and acceptability. Patients improved with moderate to large effect sizes on eating disorder symptoms, weight, self-criticising and self-reassuring. However, no effect was statistically significant. Results suggest that group CFT as an adjunct to day patient program for eating disorders may be a feasible and acceptable treatment that may contribute to the recovery of patients with eating disorders.

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

Psykisk ohälsa hos ungdomar är ett växande problem och tonårstiden är en sårbar period för utveckling av bland annat stress, ångest och depression, tillstånd där skam och självkritik ofta ingår. Vidare har svårigheter att reglera känslor identifierats som en orsak till psykiska problem. Compassionfokuserad terapi (CFT) är en behandlingsform som har tagits fram för att fånga upp patienter som upplever skam och självkritik och metoden har god evidens för en vuxen population. Däremot finns det färre studier där behandlingens utfall undersökts för ungdomar, i synnerhet forskning där ungdomarnas egna erfarenheter av terapin studerats. Syftet med denna kvalitativa studie var att undersöka upplevelser av känslor efter avslutad compassionfokuserad gruppbehandling hos ungdomar med lindrig till måttlig grad av stress, ångest och depression. Tjugosex deltagare, 21 kvinnor, tre män och två icke-binära, i åldersgruppen 15-20 år intervjuades i fokusgrupper, och materialet analyserades med tematisk analys. I analyserna framkom olika beskrivningar av känslor som tolkades i fem teman: Förståelse för sig själv, Förändring, Gruppallians, Upplevelsebaserat och Värna Kroppen. Analysen ledde till slutsatser avseende deltagarnas beskrivningar av känslor som indikerar att olika dimensioner i den compassionfokuserade behandlingen har påverkat deltagarnas förmåga att känna trygghet och medvetandegöra känslor. Möjligheter att skifta perspektiv, få en ökad förståelse för sig själv, känna social tillhörighet, uppleva medveten närvaro och förstå kroppsliga sensationer kan bidra till ökad compassion vilket i sin tur kan påverka förmågan att förstå och reglera känslor. / Mental health issues among adolescents are a growing concern, and adolescence is a vulnerable period for the development of stress, anxiety and depression, conditions which often involve elements of shame and self-criticism. Difficulties with emotion regulation have been identified as a cause of mental health problems. Compassion-Focused Therapy (CFT) has been developed to help patients who experience shame and self-criticism, and there is significant evidence that supports its efficiency in an adult population. However, only a few studies have investigated treatment outcomes for adolescents, particularly those examining the youths’ own experience of therapy. The aim of this qualitative study was to explore the experiences of emotions after completing a compassion-focused treatment in a group of adolescents with mild to moderate levels of stress, anxiety and depression. Twenty-six participants, 21 females, three males, and two non-binary individuals, aged 15-20 years were interviewed in focus groups, and the material was analyzed using thematic analysis. In the analysis different descriptions of the participants' emotions emerged, which was interpreted into five themes: Self-Understanding, Change, Group Alliance, Experience-Based, and Care of the Body. The analysis led to conclusions about the participants' descriptions of emotions, which indicate that different dimensions of the compassion-focused treatment have influenced the participants’ ability to feel secure and be aware of their emotional experience. The opportunity to shift perspective, increase self-understanding, feel social belonging, experience mindfulness and understand bodily sensations may contribute to increased compassion and capacity to understand and regulate emotions.

In this thesis we investigate the quantum aspects of black holes near extremality. In particular we seek evidence that a near-extremal black hole has a microscopic description in terms of a two dimensional conformal field theory (CFT). We first demonstrate how the low temperature expansion of the first law of thermodynamics leads to an expression for the entropy of extremal black holes which can be recast as the Cardy formula for the entropy of a chiral two dimensional CFT, in agreement with the Extremal Black Hole/CFT correspondence. We apply Sen’s entropy function formalism to fortify this result by reproducing it in a gravitational setup. We extend our first law analysis to a class of near-Extremal Vanishing Horizon (near-EVH) black holes. These black holes have low entropy and temperature, and their geometries contain locally asymptotically AdS3 throats in the near horizon region. The low temperature expansion of the first law is compatible with the first law for a three dimensional BTZ black hole. As the BTZ black hole has an AdS/CFT description in terms of a non-chiral two dimensional CFT, our result can be viewed as thermodynamic evidence for the EVH/CFT correspondence, which states that gravity on the near horizon EVH geometry is described by a 2d CFT. A near-EVH black hole, or low energy excitation around an EVH black hole, is described by excitations of the dual 2d CFT. As case studies of our first law analysis and the EVH/CFT correspondence, we focus on two asymptotically AdS5× S5 classes of near-EVH black holes. The two cases have interesting individual properties and, by the AdS/CFT correspondence, dual descriptions as states in N = 4 super Yang-Mills theory . We can compare these (UV) pictures to the two dimensional descriptions that emerge from the near horizon, or low energy, dynamics. All EVH near horizon geometries have local AdS3 factors which become BTZ black holes when the configurations are excited from EVH to near-EVH. In the study of static black holes with three R-charges, we examine the non-BPS and near- BPS regimes separately. While the non-BPS near horizon limit is locally regular, in the near- BPS case the near horizon procedure requires focussing geometrically on a strip of the horizon, and the degrees of freedom of the dual CFT2 can be associated with stretched strings between giant gravitons in the transverse five-sphere. The near-EVH limit of non-BPS stationary charged black holes is obtained by taking the vanishing limit of one or both of the angular momenta. When one of the momenta is small, the AdS3 angle is a combination of azimuthal angles in the AdS5 and S5 regions of the geometry. Taking the vanishing limit of both of the angular momenta leads to a near horizon limit which contains a BTZ black hole that is non-trivially fibred by a three-sphere. For each of the case studies we use the AdS3/CFT2 dictionary to specify dual IR CFT2 descriptions of the black holes. We outline a map between the UV and IR near-EVH excitations and demonstrate how the first law reduces in the near-EVH limit to the first law of a BTZ black hole. As a consistency check we compare our results with those of the Kerr/CFT correspondence.

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.

La théorie des cordes est le candidat le plus promettant pour la théorie unissant toutes les interactions en incluant la gravitation. Elle a la dynamique très compliquée. C'est pourquoi c'est utile d'étudier ses simplifications. Une de celles-ci est la théorie des cordes non-critiques qui peut être définie dans les dimensions inférieures. Le cas particulièrement intéressant est la théorie des cordes à deux dimensions. D'une part elle a la structure très riche et d'autre part elle est résoluble exactement. La solution complète de la théorie des cordes à deux dimensions dans le fond le plus simple du dilaton linéaire a été obtenue en utilisant sa représentation comme la mécanique quantique matricielle. Ce modèle de matrices fournit une technique très puissante et découvre l'intégrabilité cachée dans la formulation habituelle de CFT. Cette thèse prolonge la formulation de la théorie des cordes à deux dimensions par des modèles de matrices dans des fonds non-triviaux. Nous montrons comment les perturbations changeants le fond sont incorporés à la mécanique quantique matricielle. Les perturbations sont intégrables et dirigées par la hiérarchie de Toda. Cette intégrabilité est utilisée pour extraire l'information divers sur le système perturbé: les fonctions des corrélations, le comportement thermodynamique, la structure de l'espace-temps. Les résultats concernant ces et autres questions, comme des effets non-perturbatifs dans la théorie des cordes non-critiques, sont présentés dans cette thèse.

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