Hydrodynamics is an effective theory that is extremely successful in describing a wide range of physical phenomena in liquids, gases and plasmas. However, our understanding of the structure of the theory, its microscopic origins and its behaviour at strong coupling is far from complete. To understand how an effective theory of dissipative hydrodynamics could emerge from a closed microscopic system, we analyse the structure of effective Schwinger-Keldysh Closed-Time-Path theories. We use this structure and the action principle for open systems to derive the energy-momentum balance equation for a dissipative fluid from an effective CTP Goldstone action. Near hydrodynamical equilibrium, we construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations. Shear viscosity is shown to vanish, while bulk viscosity and thermodynamical quantities are determined by the form of the effective action. The exploration of strongly interacting states of matter, particularly in the hydrodynamic regime, has been a major recent application of gauge/string duality. The strongly coupled theories involved are typically deformations of large-$N$ SUSY gauge theories with exotic matter that are unusual from a low-energy point of view. In order to better interpret holographic results, an understanding of the weak-coupling behaviour of such gauge theories is essential. We study the exact and SUSY-broken N=1 and N=2 super-QED with finite densities of electron number and R-charge, respectively. Despite the fact that fermionic fields couple to the chemical potentials, the strength of scalar-fermion interactions, fixed by SUSY, prevents a Fermi surface from forming. This is important for hydrodynamical excitations such as zero sound. Intriguingly, in the absence of a Fermi surface, the total charge need not be stored in the scalar condensates alone and fermions may contribute. Gauss-Bonnet gravity is a useful laboratory for non-perturbative studies of the higher derivative curvature effects on transport coefficients of conformal fluids with holographic duals. It was previously known that shear viscosity can be tuned to zero by adjusting the Gauss-Bonnet coupling, λ_GB, to its maximal critical value. To understand the behaviour of the fluid in this limit, we compute the second-order transport coefficients non-perturbatively in λ_GB and show that the fluid still produces entropy, while diffusion and sound attenuation are suppressed at all order in the hydrodynamic expansion. We also show that the theory violates a previously proposed universal relation between three of the second order transport coefficients. We further compute the only second-order coefficient thus far unknown, λ₂, in the N=4 super Yang-Mills theory with the leading-order 't Hooft coupling correction. Intriguingly, the universal relation is not violated by these leading-order perturbative corrections. Finally, by adding higher-derivative photon field terms to the action, we study charge diffusion and non-perturbative parameter regimes in which the charge diffusion constant vanishes.

No presente trabalho foi analisado o comportamento de ligações viga-pilar em estruturas mistas de aço e concreto com o auxílio de simulação numérica e experimentação. A simulação numérica foi realizada no programa DIANA, baseado no método dos Elementos Finitos. Os modelos de ligações analisados são compostos por ligações com parafusos passantes entre pilares metálicos preenchidos com concreto e vigas metálicas. A laje utilizada foi do tipo com fôrma de aço incorporada, com a utilização de conectores de cisalhamento para resistir aos esforços em conjunto com a viga. Para simular a situação de pilar intermediário, foram utilizados modelos com formato cruciforme, os quais foram submetidos à força cíclica reversível com a finalidade de submeter à estrutura a esforços semelhantes aos provocados por vento e sismo. Além do efeito da força cíclica, este trabalho avaliou também a influência na rigidez da ligação causada pela taxa de armadura da laje e pelo detalhe de ancoragem da armadura de continuidade ao pilar misto. Para isso foram ensaiados quatro modelos. Dentro da metodologia proposta, obteve-se numérica e experimentalmente, dados que permitiram a construção de curvas momento versus rotação e força versus deslocamento para a quantificação da rigidez e determinação da ductilidade da ligação. Como resultado das análises concluiu-se que a laje contribui mais na rigidez da ligação quando ela está submetida a momento fletor positivo e com relação ao método de ancoragem não houve diferença significativa nas rigidezes. / This research studied the behavior of beam-column connection in composite steel-concrete structures and was developed with the use of numerical simulation and experimentation. The numerical simulation was performed using the program DIANA which is based on the finite element method. The models are composed of connections with bolts passing through the concrete filled tube (CFT) column and steel beams with a steel deck. It was used shear connectors for the slab works together with the beam to resist the bend. To simulate the situation of the middle column, they are used models with cruciform form, which were subjected to reversible cyclic loading in order to bring structure the efforts similar to those caused by wind and earthquake. Besides the effect of cyclic loading, this research also evaluated the influence on the connection stiffness caused by the slab reinforcement ratio and anchors detail to the column of some bars. To obtain this information four models were tested. Within the proposed methodology numerical and experimental data were obtained which made possible the construction of moment versus rotation curves and loading versus displacement for the quantification of stiffness and ductility of the connections. The result of this research shows that the slab contributes more on the increase of stiffness when the connection is subjected to sagging moment and about the method of anchoring, there is no significant difference on stiffness between the two methods.

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.

One of the main topics in the modern String Theory are the conjectured string/gauge (AdS/CFT) dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality.The first part of this thesis is focused on the gravity side of the AdS5/CFT4 duality: we investigate the quantum integrability of the type IIB superstring on AdS5 x S5. In the pure spinor formulation we analyze the operator algebra by computing the operator product expansion of the Maurer-Cartan currents at the leading order in perturbation theory. With the same approach at one loop order, we show the path-independence of the monodromy matrix which implies the charge conservation law, strongly supporting the quantum integrability of the string sigma-model. We also verify that the Lax pair field strength remains well-defined at one-loop order being free from UV divergences. The same string sigma-model is analyzed in the Green-Schwarz formalism in the near-flat-space (NFS) limit. Such a limit remarkably simplifies the string world-sheet action but still leaving interesting physics. We use the NFS truncation to show the factorization of the world-sheet S-matrix at one-loop order. This property defines a two-dimensional field theory as integrable: it is the manifestation of the higher conserved charges. Hence, we have explicitly checked their presence at quantum level. The second part is dedicated to the AdS4/CFT3 duality: in particular the type IIA superstring on AdS4 x CP3. We compute the leading quantum corrections to the string energies for string configurations with a large but yet finite angular momentum on CP3 and show that they match the conjectured all-loop Bethe Ansatz equations.

This dissertation splits into two distinct halves. The first half is devoted to the study of the holography of higher spin gauge theory in AdS$_3$. We present a conjecture that the holographic dual of $W_N$ minimal model in a 't Hooft-like large $N$ limit is an unusual ``semi-local" higher spin gauge theory on AdS$_3\times $S$^1$. At each point on the S$^1$ lives a copy of three-dimensional Vasiliev theory, that contains an infinite tower of higher spin gauge fields coupled to a single massive complex scalar propagating in AdS$_3$. The Vasiliev theories at different points on the S$^1$ are correlated only through the AdS$_3$ boundary conditions on the massive scalars. All but one single tower of higher spin symmetries are broken by the boundary conditions. This conjecture is checked by comparing tree-level two- and three-point functions, and also one-loop partition functions on both side of the duality. The second half focuses on the holography of higher spin gauge theory in AdS$_4$. We demonstrate that a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS$_4$ admits boundary conditions that preserve ${\cal N}=0,1,2,3,4$ or $6$ supersymmetries. In particular, we argue that the Vasiliev theory with $U(M)$ Chan-Paton and ${\cal N}=6$ boundary condition is holographically dual to the 2+1 dimensional $U(N)_k\times U(M)_{-k}$ ABJ theory in the limit of large $N,k$ and finite $M$. In this system all bulk higher spin fields transform in the adjoint of the $U(M)$ gauge group, whose bulk t'Hooft coupling is $\frac{M}{N}$. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS$_4\times \mathbb{CP}^3$, and that the non-Abelian Vasiliev theory at strong bulk 't Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev's higher spin particles held together by $U(M)$ gauge interactions. / Physics

No presente trabalho foi analisado o comportamento de ligações viga-pilar em estruturas mistas de aço e concreto com o auxílio de simulação numérica e experimentação. A simulação numérica foi realizada no programa DIANA, baseado no método dos Elementos Finitos. Os modelos de ligações analisados são compostos por ligações com parafusos passantes entre pilares metálicos preenchidos com concreto e vigas metálicas. A laje utilizada foi do tipo com fôrma de aço incorporada, com a utilização de conectores de cisalhamento para resistir aos esforços em conjunto com a viga. Para simular a situação de pilar intermediário, foram utilizados modelos com formato cruciforme, os quais foram submetidos à força cíclica reversível com a finalidade de submeter à estrutura a esforços semelhantes aos provocados por vento e sismo. Além do efeito da força cíclica, este trabalho avaliou também a influência na rigidez da ligação causada pela taxa de armadura da laje e pelo detalhe de ancoragem da armadura de continuidade ao pilar misto. Para isso foram ensaiados quatro modelos. Dentro da metodologia proposta, obteve-se numérica e experimentalmente, dados que permitiram a construção de curvas momento versus rotação e força versus deslocamento para a quantificação da rigidez e determinação da ductilidade da ligação. Como resultado das análises concluiu-se que a laje contribui mais na rigidez da ligação quando ela está submetida a momento fletor positivo e com relação ao método de ancoragem não houve diferença significativa nas rigidezes. / This research studied the behavior of beam-column connection in composite steel-concrete structures and was developed with the use of numerical simulation and experimentation. The numerical simulation was performed using the program DIANA which is based on the finite element method. The models are composed of connections with bolts passing through the concrete filled tube (CFT) column and steel beams with a steel deck. It was used shear connectors for the slab works together with the beam to resist the bend. To simulate the situation of the middle column, they are used models with cruciform form, which were subjected to reversible cyclic loading in order to bring structure the efforts similar to those caused by wind and earthquake. Besides the effect of cyclic loading, this research also evaluated the influence on the connection stiffness caused by the slab reinforcement ratio and anchors detail to the column of some bars. To obtain this information four models were tested. Within the proposed methodology numerical and experimental data were obtained which made possible the construction of moment versus rotation curves and loading versus displacement for the quantification of stiffness and ductility of the connections. The result of this research shows that the slab contributes more on the increase of stiffness when the connection is subjected to sagging moment and about the method of anchoring, there is no significant difference on stiffness between the two methods.

Établir une théorie de gravité quantique qui décrit de manière cohérente les propriétés quantiques de la matière et de l'espace-temps est l'un des défis majeurs de la physique théorique. Malgré plusieurs décennies de recherches, de nombreux problèmes conceptuels et techniques doivent encore être résolus. L'étude de modèles simplifiés donne des idées de résolution. La première partie de la thèse traite de la gravité quantique bidimensionnelle. À deux dimensions, la gravité quantique est beaucoup mieux comprise et de nombreux calculs peuvent être faits exactement. Si la gravité quantique bidimensionnelle a été largement étudiée quand elle est couplée à de la matière conforme, le cas de la matière non-conforme était très peu connu jusque récemment. Nous calculons d'abord l'action gravitationnelle pour un champ scalaire massif sur une surface de Riemann avec bords puis pour un fermion de Majorana massif sur une variété compacte. Ce dernier cas correspond à une CFT perturbée par une perturbation conforme et est d'ordinaire étudié grâce à l'ansatz de DDK, mais les résultats sont différents. Finalement, on calcule le spectre de l'action de Mabuchi dans l'approximation du minisuperespace. La seconde partie étudie les propriétés thermales des trous noirs dans le contexte de la correspondance AdS/CFT. On construit un modèle de mécanique quantique fondé sur les principes holographiques pour simuler la dynamique des trous noirs quantiques. Ce modèle permet d'obtenir des résultats numériques exacts. / Finding a theory of quantum gravity describing in a consistent way the quantum properties of matter and spacetime geometry is one of the greatest challenges of modern theoretical physics. However after several decades of research, many conceptual and technical issues are still to be resolved. Insights on these questions can be given by simplified toy models that allow for exact computations. The first part of the thesis deals with two-dimensional quantum gravity. In two dimensions quantum gravity is much better understood and many computations can be carried out exactly. Whereas two-dimensional quantum gravity coupled to conformal matter has been widely studied and is now well understood, much less was known until recently when matter is non-conformal. First we compute the gravitational action for a massive scalar field on a Riemann surface with boundaries and then for a massive Majorana fermion on a manifold without boundary. The latter case corresponds to a CFT perturbed by a conformal perturbation and is usually tackled through the DDK ansatz, but the results do not seem to match. Finally we give a minisuperspace computation of the spectrum of the Mabuchi action, a functional that appears in the gravitational action for a massive scalar field. In the second part we focus on black hole thermal behaviour which provides a lot of insight of how a theory of quantum gravity should look like. In the context of string theory the AdS/CFT correspondence provides powerful tools for understanding the microscopic origin of black holes thermodynamics. We construct a quantum mechanical toy model based on holographic principles to study the dynamics of quantum black holes.

The work done in this thesis includes an exploration of both the conformal field theory techniques and holographic techniques of the Gauge/Gravity duality. From the field theory, we have analyzed the analytical aspects of the Conformal Bootstrap program to gain handle on at least a part of the CFT spectrum. The program applies equally to the strongly coupled as well as the weakly coupled theories. We have considered both the regimes of interest in this thesis. In the strongly coupled sector, as we have shown that it is possible to extract information about the anomalous dimensions, of a particular subset of large spin operators in the spectrum, as a function of the spin and twist of these operators. The holographic analog of the anomalous dimensions from CFT are the binding energies of generalized free fields in the bulk, which has also been analyzed in this thesis. On the contrary, in the weakly coupled sector, the same idea can be used to calculate the anomalous dimensions of operators, with any spin and dimension in an expansion. We have considered a simple set of scalar operators, whose anomalous dimensions are reproduced correctly up to O( 2). In another holographic calculation, we have analyzed generic higher derivative theories of gravity, which corresponds to boundary theories with in finite colors but finite `t Hooft coupling. Certain universal aspects of these theories, such as anomalies and correlation functions are also calculated. The three point functions for these higher derivative theories will serve as a building block for considering four point functions for finitely coupled boundary CFTs. In the conclusion, we have pointed out the directions of interest which could be locating the bulk duals of large N finitely coupled theories, or that of an intermediate theory with both finite `t Hooft coupling as well as finite gauge group, with a speculative string theory dual.

La recherche de solutions du vide en présence de flux non-triviaux dans la théorie des cordes est importante pour la construction de modèles pertinents à la phénomenologie de la physique des particules. Dans le cadre de la correspondance AdS/CFT, les théories de jauge en 4d, considérées comme descendantes de N=4 SYM, sont duales à des configurations de champs en 10d avec des géometries ayant un facteur AdS_5 asymptotiquement. Dans cette thèse, nous étudions des déformations de masse qui brisent la supersymétrie (partiellement ou totalement) du côté de la théorie des champs et qui sont duales aux états de la théorie IIB avec flux non-nuls du côté gravitique. Les équations du mouvement de la supergravité contraignent les paramètres de la théorie de jauge à satisfaire certaines relations. En particulier, nous trouvons que la somme des carrés de la masse des bosons est égale à celle fermions, rendant ces modèles problematiques pour des applications phénomenologiques. L'étude des théories duales de supergravité pour des déformations plus générales de la théorie conforme des champs exige des techniques qui vont au-delà des outils géometriques standards. La Géometrie Généralisée Exceptionelle fournit une façon très élégante d'intégrer les flux de supergravité dans la géometrie. Nous examinons les solutions AdS_5 avec des flux génériques conservants huit supercharges et nous montrons que celles-ci satisfont des relations particulièrement simples qui ont une interprétation géometrique dans le cadre de la Géometrie Généralisée. Ceci ouvre la voie pour l'étude systématique des déformations marginales supersymétriques de la théorie / The search for string theory vacuum solutions with non-trivial fluxes is of particular importance for the construction of models relevant for particle physics phenomenology. In the framework of the AdS/CFT correspondence, four-dimensional gauge theories which can be considered to descend from N = 4 SYM are dual to ten- dimensional field configurations with geometries having an asymptotically AdS_5 factor. In this Thesis, we study mass deformations that break supersymmetry (partially or entirely) on the field theory side and which are dual to type IIB backgrounds with non-zero fluxes on the gravity side. The supergravity equations of motion constrain the parameters on the gauge theory side to satisfy certain relations. In particular, we find that the sum of the squares of the boson masses should be equal to the sum of the squares of the fermion masses, making these set-ups problematic for phenomenology applications. The study of the supergravity duals for more general deformations of the conformal field theory requires techniques which go beyond the standard geometric tools. Exceptional Generalized Geometry provides a very elegant way to incorporate the supergravity fluxes in the geometry. We study AdS_5 backgrounds with generic fluxes preserving eight supercharges and we show that these satisfy particularly simple relations which admit a geometrical interpretation in the framework of Generalized Geometry. This opens the way for the systematic study of supersymmetric marginal deformations of the conformal field theory in the context of AdS/CFT.

Dans cette thèse, nous présentons des constructions explicites de la correspondance AdS/CFT dans le contexte de la théorie des cordes de type II. Ces constructions sont visées à mieux comprendre aspects de la physique nonperturbative de théories des champs superconformes à d = 6,5,4 dimensions. Dans la première partie de la thèse nous introduisons les systèmes de NS5-Dp-D(p+2)-branes de Hanany-Witten, au moyen desquels on peut construire théories des champs avec 8 supercharges. Quand p = 6, le système de NS5-D6-D8-branes permet de construire théories des champs superconformes à 6 dimensions, caractérisées par des multiplets tenseur, vecteur et hypermultiplets de la superalgèbre chirale N = (1,0). Ces théories sont décrites par des «quivers» linéaires; nous analysons en détails leurs propriétés. Dans le cadre de la correspondance AdS/CFT, une théorie superconforme à (d - 1) dimensions décrit la même physique qu’un vide de la théorie des cordes de type II compactifiée sur un espace-temps Anti-de Sitter à d dimensions (AdSd). Par le biais de la géométrie complexe généralisée nous reformulons les équations qui doivent être résolues pour trouver ces vides AdS. La seconde partie contient les contributions originales. Nous présentons une classification exhaustive des vides de la théorie des cordes de type II compactifiée sur AdS7. En type IIB, il n’y a aucun vide; en type IIA massif, nous construisons une nouvelle classe infinie (et analytique) de vides. L’espace interne est topologiquement une 3-sphere, déformée par la présence de D6 et D8-branes. Les isométries de cet espace réalisent la symétrie R des théories superconformes N = (1,0) à 6 dimensions. Nos vides AdS7 sont les duaux holographiques de ces dernières, et peuvent être obtenus par une limite près de l’horizon des systèmes de NS5-D6-D8-branes. Le second résultat est la construction d’une classe infinie de vides analytiques AdS5 en type IIA massif. L’espace interne est le produit d’une 3-sphere par une surface de Riemann. Les isométries de cet espace réalisent la symétrie R des théories superconformes N = 1 à 4 dimensions, dont nos vides AdS5 sont les duaux holographiques. Nous décrivons une bijection entre ces derniers et les vides AdS7 susmentionnés. L’interprétation holographique indique que les théories N = 1 à 4 dimensions sont obtenues en compactifiant celles N = (1,0) à 6 dimensions sur la même surface de Riemann. Troisièmement, nous réduisons à deux equations différentielles le problème de classification des vides AdS6 en type IIB duaux à théories superconformes N = 1 à 5 dimensions. L’espace interne de ces vides contient une 2-sphere, réalisant la symétrie R des ces dernières. / In this thesis we present explicit constructions of the AdS/CFT correspondence obtained from type II string theory. These constructions are aimed at studying aspects of the nonperturbative physics of 6d, 5d, 4d SCFTs. In the first part we introduce NS5-Dp-D(p+2) Hanany--Witten brane systems, capable of engineering field theories with 8 Q supercharges. In particular, when p=6, the NS5-D6-D8 brane systems are known to engineer 6d SCFT featuring tensor, vector and hypermultiplets of the chiral N=(1,0) superalgebra. These theories can be described by linear quivers. We analyze in detail their properties. In AdS/CFT, the same physics can be equivalently described by a (d-1)-dimensional SCFT and by type II string theory compactified on a d-dimensional AdS space (AdSd), giving rise to a so-called AdSd vacuum. By using techniques derived from generalized complex geometry we reformulate the equations that need to be satisfied in order to find these AdS vacua. The second part of the thesis contains the original contributions. We present a full classification of vacua of type II string theory compactified on AdS7. In type IIB there are no such vacua; in massive type IIA, we construct a new infinite class of (analytic) vacua. The internal space is topologically a three-sphere, deformed by the presence of D6 and D8-branes. The isometries of this space realize the R-symmetry of the 6d (1,0) SCFTs. Our AdS7 vacua are the holographic duals of the latter, and can be obtained via a near-horizon limit of the NS5-D6-D8 brane systems. The second result is the construction of an infinite class of analytic AdS5 vacua of massive IIA. The internal space is a fibration of a (distorted) three-sphere over a Riemann surface. Its isometries realize the R-symmetry of putative 4d N=1 SCFTs, holographically dual to our AdS5 vacua. We describe a universal one-to-one map between the latter and the aforementioned AdS7 vacua. The natural interpretation of this is that the 4d N=1 SCFTs can be obtained by compactifying (in a twisted way) the 6d (1,0) ones on the same Riemann surface. In the third and last part, we reduce to two PDEs the classification problem of AdS6 vacua of type IIB supergravity, which should be the holographic duals to 5d N=1 SCFTs. The latter can be engineered by webs of (p,q)-fivebranes in type IIB string theory. The internal space of the AdS6 vacua is given by a fibration of a round two-sphere over a two-dimensional surface; the isometries of the fibers should realize the R-symmetry of the dual field theories. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished