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How can we understand complex quantum many-body systems without finding exact solutions? Recent developments have shown that first principle constraints can provide satisfactory or even accurate estimates for quantum observables in interacting many-body systems. This dissertation summarizes a series of results centered on implications of locality in quantum dynamics and thermodynamics. We first discuss microscopic locality bounds on quantum transport, chaos and ground states in open and closed lattice models. Such locality bounds provide useful and rigorous information in strongly interacting systems. Then we consider the problem of emergent locality in holographic theories, with analytical and numerical examples in holographic tensor networks and matrix quantum mechanics. Emergent locality and causality are detected and analyzed, augmenting our microscopic understanding of holography

There is a lot of evidence that black holes follow the usual rules of quantum mechanics, and exhibit all of the fundamental properties of quantum systems such as a discrete set of energy levels. However, many of these properties are difficult to see directly in gravity; there is an apparent tension between the gravitational description of black holes in terms of smooth geometry and the discrete 'quantum' aspects of quantum mechanics. In this work we focus on understanding certain probes of the discreteness of the black hole energy spectrum which exhibit this tension, such as an averaged version of the two-point function of operators widely separated in time outside of a black hole in AdS space. The chaotic dynamics of black holes indicates that its energy levels should have random matrix statistics, and its energy eigenstates should obey the Eigenstate Thermalization Hypothesis. These expectations allow us to make precise predictions for the behavior of our probes. We find strong evidence that contributions from spacetime geometries with nontrivial topology, and even arbitrary numbers of disconnected components, are responsible for reproducing the expected behavior of our probes. Physically, these contributions correspond to including effects from the absorption and emission of closed 'baby' universes from the black hole spacetime. These processes have a small amplitude, but may provide the dominant contribution to the transitions between very distinct states of the black hole

Broadly speaking, this thesis concerns itself with diverse routes to understanding the reconciliation of gravity and quantum mechanics. Pervasive to the various topics explored lies the idea that spacetime is best understood as an emergent concept. Indeed, many past inquiries regarding the microscopic nature of the fabric of spacetime ended in deep paradoxes, the most famous being how the dynamics of black holes is to be understood in a way compatible with unitary time evolution. Fundamental to the emergent spacetime paradigm is the conclusion that the general relativistic notion of spacetime itself fails to even make sense at the smallest of distance scales. Instead, it should be replaced with a collection of non-geometric degrees of freedom. Much in the same way statistical mechanics exposed the macroscopic notions of heat and temperature as average quantities describing the motion of millions of millions of atomic particles, gravity should perhaps best be conceived as the hydrodynamics of these non-geometric variables. The articulation of the holographic principle in \cite{susskind1995world, hooft1993dimensional} sharpened these somewhat philosophical musings, appealing to the Bekenstein-Hawking entropy of black holes. In a nutshell, should one try to estimate the upper bound on the number of degrees of freedom needed to describe the physics in some finite patch of spacetime, one might imagine cramming in more and more "stuff" into said region, rendering the dynamics as complicated as possible. Eventually, the mass of the constituents reaches it equivalent Schwarzschild radius and forms a black hole. Black holes carry an associated entropy, proportional not to their volume but to their bounding area (or its higher/lower-dimensional analogues). This entropy can in turn be used to estimate the dimension of the Hilbert space one might like to associate to this region. Given the number of degrees of freedom scales not as the volume but rather as the area, it is clear the underlying theory cannot be a quantum field theory local to this patch, like those describing all other known fundamental forces. The advent of the BFSS Matrix theory \cite{banks1997m} and the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence \cite{Maldacena:1997re} provided concrete examples of the holographic principle. The AdS/CFT duality posits a non-gravitational quantum mechanical theory, not so different from those familiar in particle physics, may be completely recast as a gravitational one, in one higher dimension. While this suspersymmetric theory is a local quantum field theory formulated on the boundary of the dual Anti-de Sitter spacetime, how these degrees of freedom encode the low-energy \textit{bulk local} physics remains a difficult question. Significant progress was made with the discovery of the Ryu-Takayangi (RT) formula, which one might consider a generalization of the Bekenstein-Hawking entropy \cite{Ryu:2006bv}. It equates the entanglement entropy of a subregion of the space on which the CFT lives with the area of the bulk minimal surface ending on the boundary of said region, plus the entanglement entropy of bulk fields across this minimal surface \cite{Faulkner:2013ana}. This quickly led to important insights on bulk reconstruction and refined the duality to a subregion-subregion duality. Indeed, entanglement wedge reconstruction states that from this restricted CFT region, we can reconstruct the bulk operators contained within the entanglement wedge (a slight generalization of the region bounded by the minimal area surface described above). While the RT formula has taught us tremendous amounts about the holographic dictionary, it is not enough to address several important points. In particular, it fails to describe the emergence of bulk local physics on scales below the AdS-radius. One intuitive way to see this is to recall the renormalization group perspective on the holographic dimension. If we imagine flowing further into the bulk, integrating out more and more CFT modes, we are eventually left with only the zero-modes. This defines a matrix quantum mechanics, living on a point. With its $N^2$ degrees of freedom, we expect it to describe a whole AdS-worth of space. Clearly, there is no sense in which we can further partition the space on which the boundary theory now lives. As such, the RT formula cannot describe sub-regions below the AdS scale. We face an analogous situation in BFSS matrix theory, our only theory of quantum gravity in flat space. BFSS being "nothing more" than the quantum mechanics of matrices, there is similarly no obvious notion of subsystems mapping onto sub-regions of the emergent spacetime. Even the very notion of a subsystem is difficult to describe, an important observation which motivated much of the work in Chapter IV. Chapter I used the simplest model of holography involving a single matrix, and reproduced the entanglement entropy of the bulk fields starting from a partitioning of purely matrix degrees of freedom. Intimately connected to the holographic renormalization program and attempts at finite-patch holography is the $T \bar{T}$-deformation of field theories \cite{McGough:2016lol, Gorbenko:2018oov, Shyam:2017znq}. \cite{Zamolodchikov:2004ce} first described the deformation of conformal field theories by the irrelevant and (in flat space) well-defined composite operator $T \bar{T}$ built out of the theory's stress tensor. \cite{McGough:2016lol} related this deformation to holography, showing that at large central charge, the deformed theory seemed to describe the holographic gravitational dual contained "inside" a region, whose size was set by the amount the seed had been deformed by. One important piece of evidence came from analysing the deformed theory's thermodynamic properties and comparing to those of a BTZ black hole in a finite, radially cutoff patch of AdS. It has been argued the $T \bar{T}$-theory is the field theory with "residual gravity" modes, which have not decoupled due to the finite size of the patch. \cite{Gorbenko:2018oov} defined an impressive new deformation aimed at constructing a de-Sitter space dual starting from an AdS-dual CFT. The work of \cite{Dubovsky:2017cnj, Dubovsky:2018bmo} further explored such a a connection to quantum gravity, by realizing the $T \bar{T}$ deformation of 2d QFTs in flat space as a coupling to a variant of 2d Jackiw-Teitelboim (JT) gravity. Chapters V and VI aim to generalize this work in two directions: first, by reproducing the $J \bar{T}$ deformation (a flow generated by a composite operator built out of a $U(1)$ current and the stress-tensor) via a coupling to a mixture of topological gravity and gauge theory, and secondly, by proposing a curved space $T \bar T$ flow using the connection to 3d gravity

The butterfly effect, as an icon for the chaotic dynamics, refers to the exponential sensitivity on the initial conditions. This phenomenon is common in daily life, e.g. it explains the difficulty of long time weather reports. For physicists, the idea of the chaotic dynamics helps to understand the ergodicity of a classical complex system and therefore is essential for the statistical mechanics and thermodynamics. In the microscopic many-body systems governed by quantum mechanics, the chaotic dynamics is also expected to be generic and ultimately helpful for the understanding of the quantum thermalization. What I will show in this dissertation is that the quantum butterfly effect could also provide precise information about the nontrivial properties of the many-body interacting systems, such as thermal transport and topological properties. I will employ two classes of solvable models: the Sachdev-Ye-Kitaev model in high dimensions and the rational conformal field theories in two dimensions to explicitly present the unexpected connection between the butterfly effect and other aspects of the model.

Machine learning using deep neural networks -- deep learning -- has been extremely successful at learning solutions to a very broad suite of difficult problems across a wide range of domains spanning computer vision, game play, natural language processing and understanding, and even fundamental science. Despite this success, we still do not have a detailed, predictive understanding of how deep neural networks work, and what makes them so effective at learning and generalization. In this thesis we study the loss landscapes of deep neural networks using the lens of high-dimensional geometry. We approach the problem of understanding deep neural networks experimentally, similarly to the methods used in the natural sciences. We first discuss a phenomenological approach to modeling the large scale structure of deep neural network loss landscapes using high-dimensional geometry. Using this model, we then continue to investigate the diversity of functions neural networks learn and how it relates to the underlying geometric structure of the solution manifold. We focus on deep ensembles, robustness, and on approximate Bayesian techniques. Finally, we switch gears and investigate the role of nonlinearity in deep learning. We study deep neural networks within the Neural Tangent Kernel framework and empirically establish the role of nonlinearity for the training dynamics of finite-size networks. Using the concept of the nonlinear advantage, we empirically demonstrate the importance of nonlinearity in the very early phases of training, and its waning role farther into optimization

This thesis studies several facets of Chern-Simons-matter theories, three-dimensional systems of great interest to many physicists. The first of these three topics deals with theories in which matter is in the bifundamental representation of the Chern-Simons gauge group, as these are the natural candidates for describing higher-spin deviations from Einstein gravity. The second subject is the physics of theories with nonunitary matter, as these (in turn) are natural descriptions of four-dimensional Einstein gravity in de Sitter space. Finally, the third topic covered concerns the nature of monopoles in these theories, and includes a novel computation of scaling dimensions of simple monopole operators in conformal Chern-Simons-fermion theories.

In this thesis, we study the emergence and dynamics of strongly interacting quantum field theories in a variety of spacetime dimensions, primarily using the holographic duality. We use the duality to probe the low energy dynamics, thermodynamics, and transport properties of such systems, with an emphasis on understanding the implications of translational symmetry breaking. After illustrating the emergence of strong dynamics in a concrete and phenomenologically motivated example, we utilize the duality to study the structure of low energy excitations in holographic systems, in particular finding instances where the low energy spectral weight has non-trivial momentum space structure. With the inclusion of translational symmetry breaking, we find explicit examples where conjectured bounds on the ratio shear viscosity to entropy density are parametrically violated, as well as evidence for new disordered strongly interacting quantum critical points with non-trivial, disorder dependent critical exponents and exotic transport behavior.

So far, the cosmic microwave background has provided most of the significant constraints on cosmological parameters, but because of Silk damping and foreground contamination, the Planck Satellite has essentially reached the limit in constraining non-Gaussianity in scalar modes with the cosmic microwave background. Fortunately, the distribution of galaxies today is correlated with the conditions present in the early universe, so large-scale structure surveys can help us understand the early universe by observing the current-day galaxy distribution. In this way, it is likely that the next leading source of cosmological information will come from large-scale structure surveys like LSST and Euclid. In order for large-scale structure to significantly improve our knowledge of the early universe, for example by constraining f_NL < 1 through bispectrum measurements, the large-scale structure observables must be understood to percent level, even in the quasi-linear regime of structure formation. Recently, a research program called the Effective Field Theory of Large-Scale Structure was launched with this purpose. In this thesis, I will develop two pieces of that program: the effective field theory in redshift space, and the description of baryonic effects in the effective field theory. Finally, I will present work which computes the first slow-roll corrections to the volume of the universe and the universal entropy bound for slow-roll eternal inflation.

This dissertation is devoted to the study of models that capture the intricate dynamics of two different physical setups: exponentially expanding universes and disordered systems. We explore late time divergences in the perturbative corrections of wavefunctions of interacting light fields on a fixed de Sitter background. The divergences are holographically interpreted as shifts in the conformal weights of dual CFT operators. We then compute functional determinants in a Euclidean CFT for various non-perturbative deformations. According to the dS/CFT correspondence, these functional determinants calculate the late time Hartle-Hawking wavefunctional of asymptotically de Sitter space in higher spin gravity as a function of the profile of the fields in the bulk. Numerical experiments suggest that upon fixing the average of the bulk scalar profile, the wavefunction becomes normalizable in all the other (infinite) directions of the deformations we study. For disordered systems, we investigate the extent to which quiver quantum mechanics models encode the complex dynamics of multicentered black holes in string theory. In a certain limit of the quiver system we display the emergence of a conformal symmetry, which mimics the emergence of conformal symmetry in the near-horizon geometries of extremal black holes. Finally, we take a Newtonian multiparticle limit of the quiver system away from the conformal regime. We study the dynamics of the system numerically to look for signs of ergodicity breaking, cages, and transitions to chaos.

String theory is arguably the best candidate for a theory of quantum gravity and unified interactions. Reconciling Einstein's theory of General Relativity with Quantum Mechanics. The theory however is best understood on Minkowski and Anti-de Sitter space-times, and not on exponentially expanding space-times with positive cosmological constant, like our own universe. There is still no satisfactory formulation of String Theory on these so called asymptotically de Sitter space times. In this thesis I will discuss certain avenues of progress towards a String Theory formulation of de Sitter space-times. Specifically, how understanding of the analytic continuations of Liouville Theory and how to gauge-fix it in the Timelike regime will aid in the understanding of the proposed FRW-CFT duality of de Sitter space. It is also discussed how non-trivial topology effects proposed Chern-Simons Matter duals of Vasiliev Higher Spin gravity theories which are important in the dS-CFT description of de Sitter Space.

In this thesis I discuss progress towards a precise mathematical description of cosmology and in particular of eternal inflation. I present a conjecture for a necessary condition for a spacetime to have a precise dual description, discuss how the dictionary of dS/CFT is more sophisticated than that of AdS/CFT, present a soluble model of eternal inflation that has a conformal boundary theory at future infinity, and discuss the implications of this model for a conjectured precise dual theory based on observers in bubbles with zero cosmological constant. The work described was done in collaboration with Leonard Susskind, Douglas Stanford, and Stephen Shenker.

Super string theory is a candidate theory for the unification of gravity and all the other forces. It is also the arena in which explicit examples of gravity duals of strongly coupled field theories are constructed. In this thesis, we explore various degrees of supersymmetry breaking for strings propagating on gravitational backgrounds which have field theory duals. We analyze a class of cascading quivers arising from near horizon limits of branes at singularities, starting with RG flows which preserve some degree of supersymmetry. We then apply this analysis to cases with supersymmetry breaking. We provide examples in which supersymmetry breaks spontaneously around a metastable groundstate and calculate some of its properties. We finally discuss string models in which supersymmetry is completely broken, including the potential phenomenological applications.

This thesis is divided to three parts. In Chapter 1 we study observational signatures of chaotic inflation with nonminimal coupling to gravity. In the next two chapters we focus on the eternal nature of inflation and the measure problem. In Chapter 2 we compare predictions of several measures in eternal versus non-eternal inflation. Finally in Chapter 3 we study the Boltzmann brain problem for the scale factor cutoff measure of eternal inflation.

Recent neutrino oscillation experiments provide proof that neutrinos are massive par- ticles, but the absolute neutrino mass scale remains unknown. Observation of neu- trinoless double beta-decay (0vBB), a hypothetical nuclear transition, would provide information on the absolute neutrino mass scale. This decay violates lepton number conservation and requires that neutrinos are massive Majorana particles. Current limits on the half-life of 0vBB are in excess of 10^25 yr. The 200 kg Enriched Xenon Observatory experiment (EXO-200) is a double beta-decay exper- iment designed to improve upon this limit. It is currently in the early stages of commissioning at the Waste Isolation Pilot Plant near Carlsbad, New Mexico. This work discusses first the use of liquid xenon as source and detector medium for double beta decay. The design and construction of EXO-200 is then presented, including a detailed prediction of detector backgrounds and sensitivity.

These collected works address several basic questions about the evolution of quantum lattice systems. While a choice of local tensor factorization of the Hilbert space is often implicit in the writing of a Hamiltonian or Lagrangian, the identification of local tensor factors is not intrinsic to the Hilbert space itself. In Chapter 1, we show that generically, the tensor factorization of the Hilbert space into local degrees of freedom is uniquely determined by the Hamiltonian, at least when such a factorization exists. In Chapter 2, we discuss how a generic local Hamiltonian may be uniquely recovered from a single eigenstate such as the ground state. In Chapter 3, we characterize when local dynamics can be generated by local Hamiltonians, providing a converse to the Lieb-Robinson bounds in one dimension. In Chapter 4, we explore the emergence of classicality in large quantum systems. In particular, we show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region, any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement

The understanding of strongly coupled many body quantum systems has been dramatically improved by the application of tools originally developed for seemingly unrelated purposes, for example quantum gravity and information theory. At the same time, to understand the possible types of information flow and properties of a quantum theory of gravity, it has become clear that one needs to understand aspects of the strongly coupled regime. In this thesis, we give three examples where the interplay of these ideas gives rise to a simple and quantitative understanding for different aspects of strongly coupled models. In Chapter 2, we make precise the idea (at high temperature) that thermalization is the loss of information about initial conditions, and in doing so explain the relationship between a quantum measure of chaos and thermalization. In Chapter 3, we explicitly compute the "size" (in terms of boundary operators) of operators deep in the bulk dual of a particular holographic (chaotic) model, and find an exact relationship between bulk symmetry generator matrix elements and size. In Chapter 4, we solve a model subject to arbitrary drive, and use it to study the formation of a wormhole, as well as more general features of the gravity dual

Some of the most-studied vacua of string theory are obtained by compactification of the 10d perturbative theories on a compact Calabi-Yau manifold. Such vacua play a central role in our understanding of string dualities, have provided a setting for the development of black hole statistical mechanics, and provide starting points for quasi-realistic string phenomenology. However, in spite of the importance of these manifolds, their defining characteristic -- their Ricci-flat metrics -- has never been determined (except for tori). This is the case even for the simplest of these manifolds -- K3 -- and until recently this provided a significant obstacle to the study of black hole statistical mechanics for many 4d string vacua with half-maximal (N=4) supersymmetry. I explain how the phenomenon of wall crossing can be exploited to solve these problems. I also describe other contexts that naturally relate string theory, geometry, and BPS state counting problems. A recurring theme will be the utility of approaching problems from a number of perspectives.

This thesis explores two major topics, quantum Shannon theory and many-body quantum chaos. The first two chapters present results in quantum Shannon theory: a quantum multiparty packing lemma and universal quantum codes for the compound quantum channel. The last chapter uses random quantum circuits and numerical methods to study the onset of random matrix behavior in many-body quantum chaotic systems.