This thesis presents a series of studies of thermalization and dissipation in a variety of strongly coupled systems. The main tool for these investigations is the Gauge/Gravity duality, which establishes a correspondence between a d+1-dimensional quantum theory of gravity and a d-dimensional quantum field theory. We study the decay rates of fluctuations around the thermal equilibrium in theories in non-commutative geometry. Rapid thermalization of such fluctuations is found and motivates the conjecture that the phenomena at the black hole horizon is described by non-local physics. In the same type of environment, we analyze the Langevin dynamics of a heavy quark, which undergoes Brownian motion. We find that the late-time behavior of the displacement squared is unaffected by the non-commutativity of the geometry. In a different scenario, we study the correlation functions in theories with quantum critical points. We compute the response of these quantum critical points to a disturbance caused by a massive charged particle and analyze its late time behavior. Finally, we analyze systems far-from-equilibrium as they evolve towards a thermal state. We characterize this evolution for systems with chemical potential by focusing on the ``strong subadditivity" property of their entanglement entropy. This is achieved on the gravity side by using time dependent functions for mass and charge in an AdS-Vaydia metric. / text

Over the past decade, the AdS/CFT correspondence has proven to be a remarkable tool to study various properties of strongly coupled field theories. In the context of the holography, Ryu and Takayanagi have proposed an elegant method to calculate entanglement entropy for these field theories. In this thesis, we use this holographic entanglement entropy to study a candidate c-theorem and entanglement entropy for singular surfaces. We use holographic entanglement entropy for strip geometry and construct a candidate c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a ‘phase transition’ as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop. Then, we turn towards studying the holographic entanglement entropy for regions with a singular boundary in higher dimensions. Here, we find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge c. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, extended singularities contribute through new linear or quadratic terms in logarithm only when the locus of the singularity is even dimensional and curved.

Over the past decade, the AdS/CFT correspondence has proven to be a remarkable tool to study various properties of strongly coupled field theories. In the context of the holography, Ryu and Takayanagi have proposed an elegant method to calculate entanglement entropy for these field theories. In this thesis, we use this holographic entanglement entropy to study a candidate c-theorem and entanglement entropy for singular surfaces. We use holographic entanglement entropy for strip geometry and construct a candidate c-function in arbitrary dimensions. For holographic theories dual to Einstein gravity, this c-function is shown to decrease monotonically along RG flows. A sufficient condition required for this monotonic flow is that the stress tensor of the matter fields driving the holographic RG flow must satisfy the null energy condition over the holographic surface used to calculate the entanglement entropy. In the case where the bulk theory is described by Gauss-Bonnet gravity, the latter condition alone is not sufficient to establish the monotonic flow of the c-function. We also observe that for certain holographic RG flows, the entanglement entropy undergoes a ‘phase transition’ as the size of the system grows and as a result, evolution of the c-function may exhibit a discontinuous drop. Then, we turn towards studying the holographic entanglement entropy for regions with a singular boundary in higher dimensions. Here, we find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge c. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singularities. In these cases, extended singularities contribute through new linear or quadratic terms in logarithm only when the locus of the singularity is even dimensional and curved.

SANTOS, Victor Pereira do Nascimento. Dinâmica de solitons em superfluidos holográficos. 2010. 62 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2010. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-06-23T20:57:29Z No. of bitstreams: 1 2010_dis_vpnsantos.pdf: 969083 bytes, checksum: 66187abe576db7775b0fcfd1ae693c87 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-06-23T21:04:21Z (GMT) No. of bitstreams: 1 2010_dis_vpnsantos.pdf: 969083 bytes, checksum: 66187abe576db7775b0fcfd1ae693c87 (MD5) / Made available in DSpace on 2015-06-23T21:04:21Z (GMT). No. of bitstreams: 1 2010_dis_vpnsantos.pdf: 969083 bytes, checksum: 66187abe576db7775b0fcfd1ae693c87 (MD5) Previous issue date: 2010 / We numerically study the formation and dynamics of domain-wall-like topological defects in superfluids, using a (3+1)-dimensional abelian Maxwell-Higgs model, under the AdS/CFT correspondence. We obtain the bulk-boundary propagators, as well as the correlation functions on the boundary for a scalar field, both in massive and non-massive cases. If we impose that the fields depends only on a boundary coordinate and the bulk radial coordinate, we obtain in the dual theory the domain wall solutions found in literature. From these solutions we found that the superfluid is characterized by two length scales, one for the order parameter and other for the charge density. We also study the change of charge density in the region near the interface of the defect, and finally we investigate the modifications needed in theory to study the dynamics of these solutions. / Neste trabalho, estudamos numericamente a formação e a dinâmica de defeitos topológicos do tipo parede de domínio em superfluidos em um modelo (3+1)-dimensional do tipo Maxwell-Higgs abeliano, no contexto da correspondência AdS/CFT. Obtemos os propagadores bulk-fronteira, assim como as funções de correlação na fronteira, para um campo escalar nos casos massivo e não-massivo. Se impusermos que os campos dependem apenas da coordenada radial no bulk e de uma coordenada na fronteira, conseguimos obter na teoria dual as soluções do tipo parede de domínio encontradas na literatura. A partir dessas soluções, estudamos suas propriedades, verificando que o superfluido é caracterizado por duas escalas de comprimento, uma para o parâmetro de ordem e outra para a densidade de carga. Estudamos também a variação da densidade de carga na região próxima à interface do defeito, e por fim, investigamos as modificações necessárias na teoria para se estudar a dinâmica dessas soluções.

Thesis advisor: Kevin Bedell / Using the AdS/CFT correspondence, it has been shown that the ratio of shear viscosity to entropy density is bounded from below in strongly coupled field theories with a gravity dual. More recently, this bound has been shown to be grossly violated in novel non-Fermi liquids and the unitary Fermi gas in the presence of superfluid fluctuations above T_c. Nevertheless, a holographic approach to such systems which break the lower bound have been strongly reliant on AdS spacetimes with massive gravitons. In this work, we propose a violation of the viscosity over entropy bound in 3+1 dimensional AdS spacetimes that support stable black hole solutions with non-zero scalar field. Such a black hole is shown to be characterized by a novel phase transition at large negative mass, where the underlying thermodynamics agrees with the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF)-like phase seen in the unitary Fermi gas near Tc and the bound is similarly broken. Such a work paves the way for a holographic description of strongly-entangled quantum fluids at high Reynolds number. / Thesis (BS) — Boston College, 2021. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Scholar of the College. / Discipline: Physics.

One of the phenomenal results emerging from string theory is the AdS/CFT correspondence or gauge-gravity duality: In certain cases a theory of gravity is equivalent to a "dual" gauge theory, very similar to the one describing non-gravitational interactions of fundamental subatomic particles. A difficult problem on one side can be mapped to a simpler and solvable problem on the other side using this correspondence. Thus one of the theories can be understood better using the other. The mapping between theories of gravity and gauge theories has led to new approaches to building models of particle physics from string theory. One of the important features to model is the phenomenon of confinement present in strong interaction of particle physics. This feature is not present in the gauge theory arising in the simplest of the examples of the duality. However this N = 4 supersymmetric Yang-Mills gauge theory enjoys the property of being integrable, i.e. it can be exactly solved in terms of conserved charges. It is expected that if a more realistic theory turns out to be integrable, solvability of the theory would lead to simple analytical expressions for quantities like masses of the hadrons in the theory. In this thesis we show that the existing models of confinement are all nonintegrable--such simple analytic expressions cannot be obtained. We moreover show that these nonintegrable systems also exhibit features of chaotic dynamical systems, namely, sensitivity to initial conditions and a typical route of transition to chaos. We proceed to study the quantum mechanics of these systems and check whether their properties match those of chaotic quantum systems. Interestingly, the distribution of the spacing of meson excitations measured in the laboratory have been found to match with level-spacing distribution of typical quantum chaotic systems. We find agreement of this distribution with models of confining strong interactions, conforming these as viable models of particle physics arising from string theory.

In the first part of this thesis we study baryonic U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Such short multiplets originate from the Kaluza-Klein compactification of eleven-dimensional supergravity on the corresponding Sasaki-Einstein seven-manifolds. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, which we classify, and propose for them field theory duals. We then study in detail the cone over the well-known Sasaki-Einstein space Q^111, which is a U(1) fibration over CP^1 x CP^1 x CP^1. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and M5 branes wrapping five-cycles in the Q^111 space. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We then study the implications of turning on a closed three-form with non-zero periods through torsion three cycles in the Sasaki-Einstein manifold. This three-form, otherwise known as torsion G-flux, non-trivially affects the supergravity dual of Higgsing, and we show that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^1,2(CP^2), which is a S^3 bundle over CP^2. We then explain how the choice of M-theory circle in the background can result in exotic renormalization group flows in the dual field theory, and study this in detail for the Sasaki-Einstein manifold Y^1,2(CP^2). We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Sasaki-Einstein Q^222 example, which is a Z_2 orbifold of Q^111 in which the free Z_2 quotient is along the R-symmetry U(1) fibre. The holographic interpretation of such instantons is currently unclear. In the second part of this thesis we study the breaking of baryonic symmetries in the AdS_5/CFT_4 correspondence for D3 branes at Calabi-Yau three-fold singularities. This leads, for particular vacuum expectation values, to the emergence of non-anomalous baryonic symmetries during the renormalization group flow. We identify these vacuum expectation values with critical values of the NS-NS B-field moduli in the dual supergravity backgrounds. We study in detail the C^3/Z_3 orbifold theory and the dual supergravity backgrounds that correspond to the breaking of the emerging baryonic symmetries, and identify the expected Goldstone bosons and global strings in the infra-red. In doing so we confirm the claim that the emerging symmetries are indeed non-anomalous baryonic symmetries.

The discovery of integrability in planar N=4 super Yang-Mills and ABJM has enabled a precise study of AdS/CFT. In the past decade integrability has been successfully applied to the spectrum of anomalous dimensions, which can now be obtained at any value of the coupling. However, in order to solve conformal field theories one also needs to understand their structure constants. Recently, there has been great progress in this direction with the all-loop proposal of Basso, Komatsu and Vieira. But there is still much to understand, as it is not yet possible to use that formalism to find structure constants of short operators at strong coupling. It is important to study wrapping corrections and resum them as the TBA did for the spectrum. It is also crucial to obtain perturbative data that can be used to check if the all-loop proposal is correct or if there are new structures that need to be unveiled. In this thesis we compute several structure constants of short operators at strong coupling, including the structure constant of Konishi with half-BPS operators. Still at strong coupling, we find a relation between the building blocks of superstring amplitudes and the tensor structures allowed by conformal symmetry. We also consider the case of extremal correlation functions and the relation of their poles to mixing with double-trace operators. We also study three-point functions at weak coupling. We take the OPE limit in a four-point function of half-BPS operators in order to shed some light on the structure of five-loop wrapping corrections of the Hexagon form factors. Finally, we take the first steps in the generalization of the Hexagon programme to other theories. We find the non-extremal setup in ABJM and the residual symmetry that it preserves, which we use to fix the two-particle form factor and constrain the four-particle hexagon. Finally, we find that the Watson equations hint at a dressing phase that needs to be further investigated.

The most general AdS$_5 imes Y$ solutions of type IIB string theory that are AdS/CFT dual to superconformal field theories in four dimensions can be fruitfully described in the language of generalized geometry, a powerful hybrid of complex and symplectic geometry. We show that the cone over the compact five-manifold $Y$ is generalized Calabi-Yau and carries a generalized holomorphic Killing vector field $xi$, dual to the R-symmetry. Remarkably, this cone always admits a symplectic structure, which descends to a contact structure on $Y$, with $xi$ as Reeb vector field. Moreover, the contact volumes of $Y$, which can be computed by localization, encode essential properties of the dual CFT, such as the central charge and the conformal dimensions of BPS operators corresponding to wrapped D3-branes. We then define a notion of ``generalized Sasakian geometry'', which can be characterized by a simple differential system of three symplectic forms on a four-dimensional transverse space. The correct Reeb vector field for an AdS$_5$ solution within a given family of generalized Sasakian manifolds can be determined---without the need of the explicit metric---by a variational procedure. The relevant functional to minimize is the type IIB supergravity action restricted to the space of generalized Sasakian manifolds, which turns out to be just the contact volume. We conjecture that this contact volume is equal to the inverse of the trial central charge whose maximization determines the R-symmetry of the dual superconformal field theory. The power of this volume minimization is illustrated by the calculation of the contact volumes for a new infinite family of solutions, in perfect agreement with the results of $a$-maximization in the dual mass-deformed generalized conifold theories.

Este é um trabalho de revisão. Os principais formalismos no desenvolvimento da teoria de cordas são introduzidos e discutidos: a corda bosônica e as supercordas no formalismo de Ramond-Neveu-Schwarz e no formalismo de Green-Schwarz. São introduzidas também as açôes efetivas no limite de baixas energias das D-branas (ação DBI) e das teorias de supergravidade (D=10,11). Por fim, são analisados alguns aspectos da correspondência AdS/CFT, enunciando a conjectura e introduzindo algumas das entradas do dicionário. Os apêndices contêm tópicos de grande relevância para o texto e podem ajudar a esclarecer vários raciocínios e passagens ao longo do mesmo. / This is a review work. The main formalisms on the development of string theory are introduced and discussed: the bosonic string and the superstrings formalisms of Ramond-Never-Schwarz and Green-Schwarz. The effective actions in the low energy limit of the D-branes (DBI action) and supergravity theories (D=10,11) are introduced as well. Finally, some aspects of the AdS/CFT correspondence are analised, enunciating the conjecture and introducing some entries of the dictionary. The appendices contains some topics that are highly relevant for the whole text and may help clarify several ideas and arguments through it.