<p> Among systems with many hard-core point particles that only interact by elastic collisions in one-dimension, it has long been thought that only those with equal mass particles were completely integrable, where the final state of the system through time evolution could be easily predicted from its initial state due to the existence of a maximal number of conserved quantities. In this thesis, we introduce a new class of integrable three-particle systems that contain two unequal masses. These integrable triplets can affect the rate of thermalization in a much larger system composed of particles with two unequal masses, the effect of which is demonstrated with a numerical simulation. </p><p>

<p>In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal window of four dimensional gauge theories with Dirac fermions and its potential applicability to beyond the standard model physics.</p><p> In the first chapter, we review some of the history of models of composite Higgs scenarios in order to motivate the study of gauge theories near the conformal window. In the second chapter we review lattice studies of a specific theory, SU(3) gauge theory with eight flavors of Dirac fermions in the fundamental representation of the gauge group. We place a particular emphasis on the light flavor-singlet scalar state appearing in the spectrum of this model and its possible role as a composite Higgs boson. We advocate an approach to characterizing nearly conformal gauge theories in which lattice calculations are used to identify the best low energy effective field theory (EFT) description of such nearly conformal gauge theories, and the lattice and EFT are then used as complementary tools to classify the generic features of the low energy physics in these theories. We present new results for maximal isospin &pi;&pi; &rarr; &pi;&pi; scattering on the lattice computed using L&uuml;scher's finite volume method. This scattering study is intended to provide further data for constraining the possible EFT descriptions of nearly conformal gauge theory. In Chapter 3, we review the historical development of chiral effective theory from current algebra methods up through the chiral Lagrangian and modern effective field theory techniques. We present a new EFT framework based on the linear sigma model for describing the low lying states of nearly conformal gauge theories. We place a particular emphasis on the chiral breaking potential and the power counting of the spurion field.</p><p> In Chapter 4, we report on a new formulation of lattice quantum field theory suited for studying conformal field theories (CFTs) nonperturbatively in radial quantization. We demonstrate that this method is not only applicable to CFTs, but more generally to formulating a lattice regularization for quantum field theory on an arbitrary smooth Riemann manifold. The general procedure, which we refer to as <i>quantum finite elements</i> (QFE), is reviewed for scalar fields. Chapter 5 details explicit examples of numerical studies of lattice quantum field theories on curved Riemann manifolds using the QFE method. We discuss the spectral properties of the finite element Laplacian on the 2-sphere. Then we present a study of interacting scalar field theory on the 2-sphere and show that at criticality it is in close agreement with the exact <i>c</i> = 1/2 minimal Ising CFT to high precision. We also investigate interacting scalar field theory on [special characters omitted] x [special characters omitted]², and we report significant progress towards studying the 3D Ising conformal fixed point in radial quantization with the QFE method. In the near future, we hope for the QFE method to be used to characterize the four dimensional conformal fixed points considered in the first half of this dissertation.</p><p>

This dissertation is split into two distinct halves. The first covers various calculations done in order gain insights on holography in de Sitter space. The dispersion relation of linear perturbations of empty de Sitter space are numerically computed as a function of the location of a hypersurface on which conformal Dirichlet boundary conditions are imposed. When the hypersurface is near the south pole, the dispersion relation is linear, whereas for a hypersurface near the cosmological horizon, it satisfies that of the incompressible Navier-Stokes equation. This result is shown to hold for non-linear perturbations. We also compute the thermodynamic stability of rotating black holes in \(dS_4\) as a function of their mass and angular momentum. We focus particularly on the rotating Nariai geometry, which is a near horizon limit of the rotating black hole as the outer and cosmological horizons tend towards each other. We study massless scalar fields in these backgrounds and obtain their quasinormal mode spectrum explicitly. We uncover an interesting structure in their two-point functions, namely that they resemble thermal Green's functions of a two-dimensional conformal field theory. The second half of this dissertation deals with the study of multicentered black holes in string theory and their finite temperature extensions. We show that there exist finite temperature single-centered solutions in \(\mathcal{N}=2\) supergravity in asymptotically flat space that admit bound states with BPS probe particles. We compute the existence regions of these bound states as well as their dependence on temperature. We embed these solutions in Fayet-Illiopoulos gauged supergravity and show that bound states persist in asymptotically \(AdS_4\) spacetimes. We make attempts to understand these disordered bound states as amorphous/glassy phases of the dual conformal field theory. / Physics

<p> Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slows down under cooling. The specific pattern of slowing down depends on the material considered. We poorly understand this dependence, in particular, which aspects of the microscopic structures control the dynamics and other macroscopic properties is unclear. Attacking this question is one of the two main aspects of this dissertation. We have introduced a new class of models of supercooled liquids, which captures the central aspects of the correspondence between structure and elasticity on the one hand, structure and thermodynamic and dynamic properties on the other. These models can also be resolved analytically, leading to theoretical insights into the question. Our results also shed new light on the temperature-dependence of the topology of covalent networks, in particular, on the rigidity transition that occurs when the valence is increased. Observations suggested the presence of a "rigidity window" where rigidity is barely satisfied and the system is near criticality. Our work rules out the predominant explanation for this phenomenon.</p><p> Other questions appear in glassy systems at zero temperature, when the thermal activation time is infinitely long. In that situation, a glassy system can flow if an external driving force is imposed above some threshold. Near the threshold, the dynamics are critical. To describe the dynamics, one must understand how the system self-organizes into specific configurations.</p><p> The first example we will consider is the erosion of a river bed. Grains or pebbles are pushed by a fluid and roll on a disordered landscape made by the static particles. Experiments support the existence of a threshold forcing, below which no erosion flux is observed. Near the threshold, the transient state takes very long and the flux converges very slowly toward its stationary value. In the field, this long transient state is called "armoring" and corresponds to the filling up of holes on the frozen landscape by moving particles. The dynamics near threshold are relevant for geophysical applications &ndash; river beds tend to spontaneously sit at the threshold where erosion stops, but are poorly understood. In this dissertation, we present a novel microscopic model to describe the erosion near threshold. This model makes new quantitative predictions for the erosion flux <i>vs</i> the applied forcing and predicts that the spatial reparation of the flux is highly non-trivial: it is power-law distributed in space with long-range correlation in the flux direction, but no correlations in the perpendicular directions. We introduce a mean-field model to capture analytically some of these properties.</p><p> To study further the self-organization of driven glassy systems, we investigate, as our last example, the athermal dynamics of mean-field spin glasses. Like many of other glasses, such as electron glasses, random close packings, etc., the spin glass self-organizes into configurations that are stable, but barely so. Such marginal stability appears in the presence of a pseudogap in soft excitations &ndash; a density of states vanishing as a power-law distribution at zero energy. How such pseudogaps appear dynamically as the systems are prepared and driven was not understood theoretically. We elucidate this question, by introducing a stochastic process mimicking the dynamics, and show that the emergence of a pseudogap is deeply related to very strong anti-correlations emerging among soft excitations.</p>

The mystery of dark matter (DM) is undeniably one of the greatest in modern physics. For decades, evidence has accumulated from astrophysical and cosmological experiments suggesting that the Universe contains a large amount of mass yet unaccounted for. In particular, present research indicates that approximately 84% of the total matter content in the Universe is non-baryonic DM. Together with the well-known limitations of the Standard Model of particle physics (SM), some of which could be remedied by theories which necessarily include additional particles, a particle physics solution to the DM problem is certainly well motivated. In this thesis the Large Hadron Collider (LHC) phenomenology of three models of DM is studied. In particular, the focus is on signals due to final states containing hadronic jets in association with a large amount of missing transverse energy, corresponding to DM which escapes detection. For the first model, it is found that studying events with one jet in the final state can allow constraints to be derived on the size of the couplings between DM and SM particles, but it is not possible to extract any information about the structure of the couplings. This motivates an analysis of events which feature two jets. For the second model, it is found that measurements of the azimuthal angular separation of these jets lead to contrasting distributions depending on the Lorentz structure of the interactions. These spectra are shown to be stable under various corrections and, more importantly, are clearly produced whether or not one performs the calculation using an effective field theory framework. For the third model, which differs from the first two in that DM now couples to the SM gauge bosons rather than the quarks, recent experimental searches are used to derive bounds on the fiducial cross sections for a variety of final states featuring missing transverse energy. This facilitates a comparison to be made between the various search strategies, identifying which of these most strongly constrain the operators under consideration. Considering the final state containing two jets, the azimuthal angular distributions are then plotted and are again found to be strongly dependent on the Lorentz structure of the underlying interactions. Prospects for the 14 TeV LHC run are then studied and it is found that a clear distinction between the spectra should be possible once 300 fb^-1 has been collected.

<p> A conformal field theory embedded in a curved spacetime background can be characterized by the trace anomaly coefficients of the stress tensor. We first derive general vacuum stress tensors of even-dimensional conformal field theories using Weyl anomalies. We then consider some aspects of conformal field theory in space-time dimensions higher than two with a codimension-one boundary. We discuss how boundary effect plays an important role in the study of quantum entanglement. We also obtain universal relationships between boundary trace anomalies and stress-tensor correlation functions near the boundary. A non-supersymmetric graphene-like conformal field theory with a four-dimensional bulk photon and a three-dimensional boundary electron is found to have two boundary central charges that depend on an exactly marginal direction, namely the gauge coupling.</p><p>

<p> In this thesis, we explore analytical methods to study conformal field theories (CFTs) in a general number of spacetime dimensions. We first use the lightcone bootstrap to systematically study correlation functions of scalar operators charged under global symmetries. We then generalize existing techniques in the lightcone bootstrap to study four-point functions containing operators with spin. As an application, we observe a close connection between anomalous dimensions of large spin, double-twist operators and the conformal collider bounds. Through further refinement of these techniques and the application of known analyticity properties for four-point functions, we also present a proof for these bounds that relies on basic physical consistency conditions. We then generalize these techniques further to study large <i>N</i> CFTs in the Regge limit and the implications of crossing symmetry in this limit. By studying the Regge limit, we can make new predictions for the large twist, large spin spectrum of CFTs and derive new bounds on CFT data. In the final part of this thesis, we use the Regge limit and constraints from unitarity to derive new bounds for both large <i>N</i> and generic CFTs. For large <i>N</i> CFTs, we derive new constraints on theories dual to a weakly-coupled, gravitational theory in an Anti-deSitter (AdS) spacetime, and for generic CFTs we derive generalizations of the conformal collider bounds. </p><p>

<p>In this thesis, we study microstate geometries of black holes in string theory and explore several aspects of integrabile Conformal Field Theories (CFTs). The first goal of this thesis is to get insights into physics of black holes by constructing a large new family of regular geometries that would account for the Bekenstein--Hawking entropy. Several classes of such states have been found in the past, but the number of known solutions is not sufficient to fully account for the entropy of macroscopic black holes. In this thesis we construct a large new family of regular microstate geometries and identify a new superposition principle for them. This feature stems from a hidden linear structure of equations governing our geometries, and it makes the dynamical system solvable or integrable. The second goal of this thesis is to explore the space of integrable string theories. Being analytically solvable, such models lead to important insights into the structure of strongly--coupled systems. While there is no algorithmic procedure for finding new integrable theories, in certain cases one can promote isolated examples into continuous families of solvable systems by performing so--called $\eta$-- and $\lambda$--deformations. In this thesis we combine the methods associated with these two deformations to construct multi--parameter families of integrable models and to explore analytical structure of the resulting theories. The third goal of this thesis is to study excitations of integrable backgrounds in string theory. The conventional approach to such analyses is based on separation of variables associated with continuous geometric symmetries, but it breaks down for the deformed models since all such symmetries are lost. Nevertheless, in this thesis we completely determine the spectra of scalar fields on several $\lambda$--deformed backgrounds by combining algebraic and group-theoretic methods.

abstract: This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1 dimensions from the perspective of a dual quantum field theory living in d dimensions. We begin by considering Rindler space which is the part of Minkowski space seen by an observer with a constant proper acceleration. Because it has an event horizon, Rindler space has been studied in great detail within the context of quantum field theory. However, a quantum gravitational treatment of Rindler space is handicapped by the fact that quantum gravity in flat space is poorly understood. By contrast, quantum gravity in anti-de Sitter space (AdS), is relatively well understood via the AdS/CFT correspondence. Taking this cue, we construct Rindler coordinates for AdS (Rindler-AdS space) in d + 1 spacetime dimensions. In three spacetime dimensions, we find novel one-parameter families of stationary vacua labeled by a rotation parameter &beta;. The interesting thing about these rotating Rindler-AdS spaces is that they possess an observer-dependent ergoregion in addition to having an event horizon. Turning next to the application of AdS/CFT correspondence to Rindler-AdS space, we posit that the two Rindler wedges in AdSd+1 are dual to an entangled conformal field theory (CFT) that lives on two boundaries with geometry R &times; Hd-1. Specializing to three spacetime dimensions, we derive the thermodynamics of Rindler-AdS space using the boundary CFT. We then probe the causal structure of the spacetime by sending in a time-like source and observe that the CFT &ldquo;knows&rdquo; when the source has fallen past the Rindler horizon. We conclude by proposing an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space. Towards the end, we consider the concept of weak measurements in quantum mechanics, wherein the measuring instrument is weakly coupled to the system being measured. We consider such measurements in the context of two examples, viz. the decay of an excited atom, and the tunneling of a particle trapped in a well, and discuss the salient features of such measurements. / Dissertation/Thesis / Ph.D. Physics 2012

<p> Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. </p><p> This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.</p><p>