The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual

We give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.Comment: 57 pages plus appendices, 6 figures. v.2: minor correction, additional references. v.3: minor addition, additional references; v.4: minor corrections; v.5: JHEP versio

Entanglement growth during thermalization in holographic systems

We derive in detail several universal features in the time evolution of entanglement entropy and other nonlocal observables in quenched holographic systems. The quenches are such that a spatially uniform density of energy is injected at an instant in time, exciting a strongly coupled CFT which eventually equilibrates. Such quench processes are described on the gravity side by the gravitational collapse of a thin shell that results in a black hole. Various nonlocal observables have a unified description in terms of the area of extremal surfaces of different dimensions. In the large distance limit, the evolution of an extremal surface, and thus the corresponding boundary observable, is controlled by the geometry around and inside the event horizon of the black hole, allowing us to identify regimes of pre-local- equilibration quadratic growth, post-local-equilibration linear growth, a memory loss regime, and a saturation regime with behavior resembling those in phase transitions. We also discuss possible bounds on the maximal rate of entanglement growth in relativistic systems.Comment: 36+11 pages, 21 figure

Statistical mechanics of a two-dimensional black hole

The dynamics of a nearly-AdS2 spacetime with boundaries is reduced to two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We demonstrate how wavefunctions for a two-sided black hole and a regularized notion of trace can be used to construct thermal partition functions, and more generally, arbitrary density matrices. We also obtain correlation functions of external operators.Comment: 33 pages + appendices; v.2: additional reference, explicit formula for two-point correlators, and other minor improvement

Dynamics of black holes in Jackiw-Teitelboim gravity

We present a general solution for correlators of external boundary operators in black hole states of Jackiw-Teitelboim gravity. We use the Hilbert space constructed using the particle-with-spin interpretation of the Jackiw-Teitelboim action, which consists of wavefunctions defined on Lorentzian AdS2. The density of states of the gravitational system appears in the amplitude for a boundary particle to emit and reabsorb matter. Up to self-interactions of matter, a general correlator can be reduced in an energy basis to a product of amplitudes for interactions and Wilson polynomials mapping between boundary and bulk interactions

Dynamics of black holes in Jackiw-Teitelboim gravity

We present a general solution for correlators of external boundary operators in black hole states of Jackiw-Teitelboim gravity. We use the Hilbert space constructed using the particle-with-spin interpretation of the Jackiw-Teitelboim action, which consists of wavefunctions defined on Lorentzian AdS2. The density of states of the gravitational system appears in the amplitude for a boundary particle to emit and reabsorb matter. Up to self-interactions of matter, a general correlator can be reduced in an energy basis to a product of amplitudes for interactions and Wilson polynomials mapping between boundary and bulk interactions

Probabilistic deconstruction of a theory of gravity, Part I: flat space

We define and analyze a stochastic process in anti-de Sitter Jackiw-Teitelboim gravity, induced by the quantum dynamics of the boundary and whose random variable takes values in $AdS_2$. With the boundary in a thermal state and for appropriate parameters, we take the asymptotic limit of the quantum process at short time scales and flat space, and show associated classical joint distributions have the Markov property. We find that Einstein's equations of the theory, sans the cosmological constant term, arise in the semi-classical limit of the quantum evolution of probability under the asymptotic process. In particular, in flat Jackiw-Teitelboim gravity, the area of compactified space solved for by Einstein's equations can be identified as a probability density evolving under the Markovian process.Comment: 48 pages, 11 figures; v.2: minor corrections and improvements, additional appendix v.3: revised for Scipost, expanded conclusion includes discussion of relationship with microscopic SYK mode

Four-point function in the IOP matrix model

The IOP model is a quantum mechanical system of a large-$N$ matrix oscillator and a fundamental oscillator, coupled through a quartic interaction. It was introduced previously as a toy model of the gauge dual of an AdS black hole, and captures a key property that at infinite $N$ the two-point function decays to zero on long time scales. Motivated by recent work on quantum chaos, we sum all planar Feynman diagrams contributing to the four-point function. We find that the IOP model does not satisfy the more refined criteria of exponential growth of the out-of-time-order four-point function.Comment: 28 pages, 10 figure

A quantum electron star

We construct and probe a holographic description of state of matter which results from coupling a Fermi liquid to a relativistic conformal field theory (CFT). The bulk solution is described by a quantum gas of fermions supported from collapse into the gravitational well of AdS by their own electrostatic repulsion. In the probe limit studied here, the Landau quasiparticles survive this coupling to a CFT.Comment: 8 pages, 7 figure