1,721,141 research outputs found
Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry
No full textWe use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in d = 4. In minimal AdS supergravity, boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended N = 4 AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving N = 1 supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary 'superpotentials', for suitably defined 'boundary superfields'. We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS/CFT correspondence
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Quantum Chaos, Operator Growth, and Holography
Full text linkThe exact role of the internal degrees of freedom (a.k.a. d.o.f.) in holography is not well-understood. Thus, in this thesis, we study a toy model of holography without space: the Sachdev-Ye-Kitaev (SYK) Model. This 0+1 theory of all possible 4-body interactions of N fermion "flavors"/"colors" features a low energy limit reproducing aspects of 1+1 Jackiw-Teitelboim gravity. First, we show that the inherent discreteness of the quantum spectrum results in universal late-time behavior due to eigenvalue repulsion. We then note that the theory's four-point functions probe the phenomenon of operator growth, where an internal d.o.f. goes on to epidemically evolve into larger products of internal d.o.f.s. In this manner where small operators smoothly grow into superpositions of increasing products of operators, we observe a sort of "size" locality, which is intimately tied with the notion of a conformal primary "descending" along its descendants. In fact, we find that the underlying structure of the SYK epidemic limits to that of a probe particle falling into a black hole. In other words, similar to how nearest neighbor interactions lead to dynamics on a flat space background, we demonstrate that many internal interactions lead to dynamics on a higher dimensional geometry
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Future Networks of Gravitational Wave Detectors: Quantum Noise and Space Detectors
Full text linkThe current network of three terrestrial interferometric gravitational wave detectors have observed ten binary black holes and one binary neutron star to date in the frequency band from 10 Hz to 5 kHz. Future detectors will increase the sensitivity by up to a factor of 10 and will push the sensitivity band down to lower frequencies. However, observing sources lower than a few Hz requires going into space where the interferometer arms can be longer and where there is no seismic noise. A new 100 km space detector, TianGO, sensitive to the frequency band from 10 mHz to 100 Hz is described. Through its excellent ability to localize sources in the sky, TianGO can use binary black holes as standard candles to help resolve the current tension between measurements of the Hubble constant. Furthermore, all of the current and future detectors, on both the ground and in space, are limited by quantum shot noise at high frequencies, and some will be limited by quantum radiation pressure at low frequencies as well. Much effort is made to use squeezed states of light to reduce this quantum noise, however classical noise and losses severely limit this reduction. One would ideally design a gravitational wave transducer that, using its own ability to generate ponderomotive squeezing due to the radiation pressure mediated interaction between the optical modes of the light and the mechanical modes of the mirrors, approaches the fundamental limits to quantum measurement. First steps in this direction are described and it is shown that it is feasible that a large scale 40 m interferometer can observe this ponderomotive squeezing in the near future. Finally, a method of removing the effects of the vacuum fluctuations responsible for the quantum noise in gravitational wave detectors and its application to testing for the presence of deviations from general relativity is described
Topological aspects of generalized gravitational entropy
Full text linkThe holographic prescription for computing entanglement entropy requires that the bulk extremal surface, whose area encodes the amount of entanglement, satisfies a homology constraint. Usually this is stated as the requirement of a (spacelike) interpolating surface that connects the region of interest and the extremal surface. We investigate to what extent this constraint is upheld by the generalized gravitational entropy argument, which relies on constructing replica symmetric q-fold covering spaces of the bulk, branched at the extremal surface. We prove (at the level of topology) that the putative extremal surface satisfies the homology constraint if and only if the corresponding branched cover can be constructed for every positive integer q. We give simple examples to show that homology can be violated if the cover exists for some values q but not others, along with some other issues
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Area/Entropy Laws, Traversable Wormholes, and the Connections Between Geometry and Entanglement
Full text linkWe study the relationship between the geometry of spacetime and quantum information. This is motivated by recent insights which suggest that geometry is an emergent phenomenon in quantum gravity, and in particular that geometry is built from quantum entanglement.Part I of this thesis is focused on the relationship between area and entropy. Area/entropy relations are ubiquitous in gravitating systems. One manifestation of this relationship comes from the AdS/CFT correspondence, which posits a duality between quantum gravity in asymptotically Anti-de Sitter space and certain quantum field theories that can be thought of as living on the boundary of the Anti-de Sitter spacetime. When the field theory has a large number of strongly coupled fields, the dual quantum gravity spacetime is described to good approximation by classical General Relativity. In this limit, the Hubeny-Rangamani-Takayanagi (HRT) formula relates the area of surfaces in the bulk spacetime to the entanglement entropy of associated subregions in the dual field theory.A second potential incarnation of the relationship between area and entropy comes in the form of black hole area laws and a more locally-defined generalization known as a holographic screens. We explore connections between these different notions of area and entropy by studying the properties of holographic screens in Anti-de Sitter space. We also study a (modified version) of HRT like surfaces attached to arbitrary boundaries (that need not be an Anti-de Sitter boundary). Part II of this thesis involves the study of traversable wormholes. Physicists have long believed that wormholes that could be crossed by an observer or signal would be impossible to build. In fact it can be shown that, with only classical matter, traversable wormholes cannot exist. While it remained possible that subtle quantum effects might be able to provide the negative energy needed to build them, there were no successful attempts at doing so. Recently, however, examples were constructed in AdS that relied on putting interactions in the dual, entangled quantum systems, and thus illustrated the intimate relation between quantum entanglement and spacetime geometry. Below, we describe a general method by which to construct traversable wormholes that can be applied to any spacetime, including asymptotically flat space. We explicitly construct several examples in AdS and in flat space, and generalize the result to construct multi-mouthed wormholes. We further use these multi-mouthed wormholes to study the entanglement structure of the spacetime they reside in
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Searching for Causality in AdS/CFT
Full text linkString theory with certain asymptotically AdS boundary conditions can be defined non-perturbatively using the AdS/CFT correspondence, which reformulates the theory in terms of a non-gravitational quantum field theory in a lower dimensional spacetime. In this way many of the subtleties of quantizing gravity are circumvented, however, the price of this simplification is that locality is no longer manifest, even in an approximate sense. In this dissertation we study features of asymptotically AdS spacetimes related to causality and search for these properties in the dual CFT description. We begin by reviewing some of the salient features of the correspondence and studying some puzzles related to the Ryu--Takayanagi conjecture. We then show that the notion of boundary causality associated with the Gao--Wald theorem implies that holographic CFT's on Minkowski space must satisfy the averaged null energy condition (ANEC). The ANEC is a quasilocal energy condition that requires the integrated null energy on a null line to be positive. Any violations of this condition in a holographic theory would result in ``causal shortcuts'' through the bulk spacetime which would allow propagation outside of the light cone in the CFT. We next study causal wedges associated with subregions of the boundary and argue that these regions of the bulk spacetime are associated with a particular coarse-graining of the CFT reduced density matrix. In particular, we conjecture that the area of the codimension-two boundary of these wedges is equal to a particular coarse-grained entropy which we name the `one-point entropy.' We present several suggestive examples in which the conjecture holds as well as a proof that it holds to leading order in a class of spacetimes with a bulk first law. In an appendix we explain how the conjecture is equivalent to a statement about the classical Einstein equation which in principle could be rigorously proven or falsified
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Heat Flows and Entanglement Entropy: Insights From and Into AdS/CFT
Full text linkThis dissertation will focus on exploring the AdS/CFT correspondence, both as a tool to probe the behavior of strongly coupled conformal field theories (CFTs) and as a fundamental duality to help us understand the holographic connection between quantum gravity and gauge theories.We will begin with an overview of this (two-part) dissertation, followed by an introduction to gravity in asymptotically locally AdS spacetimes.In the first part of the dissertation, we will then discuss the use of AdS/CFT as a tool to probe the dynamics of heat transport in strongly coupled CFTs. We will begin with a simple case in three bulk spacetime dimensions, and then construct a four-dimensional black hole solution which is dual to heat flow in a three-dimensional CFT. This black hole solution is stationary, but its horizon is not a Killing horizon, making it an interesting gravitational solution in its own right. We will then construct the gravitational dual to a CFT on a rotating black hole, and find that the CFT does not carry heat away from the black hole, but rather is confined to a halo around it. This is an artefact of strong coupling, and we comment on possible connections to soft condensed matter phenomena.In the second part of this dissertation, we probe the AdS/CFT dictionary via entanglement entropy. Specifically, we show that the Hubeny-Rangamani-Takayanagi (HRT) prescription, which is a prescription for computing CFT entanglement entropy holographically, requires modification. We comment on possible modifications, and explore in depth the possibility of using complexified surfaces in the HRT prescription. Finally, we will approach the issue of bulk reconstruction via hole-ography, which attempts to reconstruct the bulk geometry from the entanglement entropy of regions of the CFT. We put some constraints on when this approach can succeed, and comment on why it might fail when it does
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Unraveling Quantum Gravity through the Gravitational Path Integral: Geometries, Entropies, and Algebras
Full text linkThe gravitational path integral has long served as a crucial tool in deciphering mysteries within quantum gravity. In recent years, studies of the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence have offered many valuable insights into comprehending those mysteries, and many fruitful results have been yielded from utilizing the gravitational path integral within the framework of AdS/CFT.This dissertation is devoted to studying certain aspects of the gravitational path integral, discussing its relation with gravitational entropies, spacetime geometries, and its algebraic aspects. We explore contexts from Euclidean to Lorentz signature, from holographic theories to general theories, with a goal of understanding quantum gravity in the real world. In Part I, we discuss the fixed-(HRT)-area states in the gravitational path integral. The fixed-area states are holographic states where the area of the Hubeny-Rangamani-Takayanagi (HRT) surface, the holographic dual of entanglement entropy for a region in the boundary CFT, is constrained to a small window when prepared by the gravitational path integral. The study of those fixed-area states helps understand quantum gravity beyond the leading semiclassical order. We first show that by decomposing a general holographic state into fixed-area states, an important subleading correction appears to the entanglement entropy near phase transitions. Then we explore the intrinsic spacetime geometries of fixed-area states under Lorentz-signature time evolution.In Part II, we study saddle-point geometries of the real-time gravitational path integral, in the context of computing holographic Renyi entropies. Unlike their Euclidean counterparts, these real-time saddles necessarily have complex metrics, giving an example where the saddle point is off the original contour of integration. We first present the formalism of this setup, illustrating the relevant variational problem, and features of the complex saddles. Then we demonstrate explicitly the structure of those saddles by showing examples in low dimensions by direct calculation. We also find that it is possible to deform the original integration contour to pass through saddles of this kind constructed in two-dimensional Jackiw-Teitelboim gravity. Finally, we show that the existence of these saddles results in a consequence which is necessary for unitarity to hold in quantum gravity.In Part III, we take a step towards explaining the origin of gravitational entropies, by utilizing the mathematical tool of von Neumann algebras. In particular, we give an explanation of the HRT formula purely from the bulk perspective, without making any reference to holography. This is done by constructing Hilbert spaces and von Neumann algebras from boundary conditions of the gravitational path integral with several natural axioms. The von Neumann algebras we find from this construction allows us to define a notion of entropy, which matches the HRT formula in the semiclassical limit. One of the axioms we assume which is crucial for the construction of von Neumann algebras -- the trace inequality, is proven in the semiclassical limit, and it leads to novel positivity conjectures for the gravitational action
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On Contours and Boundary Conditions for the Gravitational Path Integral
Full text linkThe gravitational path integral has been a useful tool in studying quantum gravity. This thesis is devoted to studying certain aspects of the gravitational path integral, discussing the choices of contours of integration and boundary conditions for the gravitational path integral, in both Euclidean and Lorentzian signatures.In Part I, we discuss the choice of contours of integration for the gravitational path integral. The Euclidean gravitational action is unbounded from below, which means we cannot take the contour of the Euclidean path integral to all real Euclidean geometries. We propose a Wick-rotation contour prescription for the Euclidean gravitational path integral, and test this prescription by computing the stability of black hole saddles and comparing it with standard thermodynamic stability. We also study contours for Lorentzian gravitational path integral, where the original contour of integration is taken to be over all real Lorentzian geometries. We use Jackiw–Teitelboim (JT) gravity as an example, and explicitly demonstrate that it is possible to deform the original contour to pass through complex saddles that reproduce the correct Renyi entropy of JT gravity. In addition, we consider more complicated wormhole geometries in Euclidean anti-de Sitter spacetimes, which resemble the wormholes that are important in ensuring the black hole Hilbert space dimension is finite. We discuss their genericity with large Euclidean sources at the conformal infinity and compute the stability of these Euclidean wormholes.In Part II, we discuss the choice of boundary conditions for the gravitational path integral. We propose a one-parameter family of boundary conditions for Euclidean gravity that yields a well-posed elliptic system, and study Euclidean stability of various saddles with such boundary conditions. These boundary conditions can be used to define a generalized thermal canonical ensemble. They are then applied in Lorentzian signature to study real-time evolution in a spherical cavity. By analyzing the quasi-normal modes of empty flat space, we demonstrate that the same boundary conditions fail to define a well-posed initial-boundary value problem in Lorentzian signature
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Black Holes and Holography: Insights and Applications
Full text linkThis dissertation focuses on the role classical black hole spacetimes play in the AdS/CFT correspondence. We begin by introducing some of the puzzles surrounding black holes, and we review their connection to strongly correlated CFT states through holography. Additionally, we detail numerical methods for constructing black hole states of non-trivial topology in three dimensions and evaluating their actions.In part I we focus on using black hole spacetimes to derive insights into holography and quantum gravity. Using numerical methods, we study a class of non-local operators in the CFT, defined via a path integral over a torus with two punctures. In particular, we are interested in determining the spectrum of such operators at various points in moduli space. In the dual gravitational theory, such an operator might be used to construct black hole spacetimes with arbitrarily high topology behind the horizon. We present evidence suggesting this fails, and along the way encounter a puzzle related to the positivity of these operators. The resolution of this puzzle lies in developing technology to better catalogue the relevant gravitational phases.Additionally, we use multi-boundary wormhole spacetimes to investigate the constraints on the subregion entanglement entropies of holographic states. We find tension with previously claimed properties of these constraints, namely that they define a polyhedral cone in the space of entanglement entropies. These results either suggest the possible existence of further unknown constraints, or the need for a more complicated construction procedure to realize the extremal states.In part II we focus on the holographic description of CFT states via black hole spacetimes, focusing on spacetimes perturbatively constructed from the planar AdS-Schwarzschild metric. First, we consider corrections to properties of confining ground states of holographic CFTs as we introduce spatial curvature. Next, we compute shifts in vacuum entanglement entropy in a thermal state with a locally varying temperature as well as similar shifts in the confining ground states with spatial curvature
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