Sunok Josephine Suh

We propose that the underlying context of holographic duality and the Ryu-Takayanagi formula is that the volume measure of spacetime is a probability measure constrained by quantum dynamics. We define quantum stochastic processes using joint quantum distributions which are realized in a quantum system as expectation values of products of projectors. In anti-de Sitter JT gravity, we show that Einstein’s equations arise from the evolution of probability under the quantum stochastic process induced by the boundary, with the area of compactified space in the gravitational theory identified as a probability density evolving under the quantum process. Extrapolating these and related results in flat JT gravity found in [SciPost Phys. 15, 174 (2023)], we conjecture that general relativity arises in the semi-classical limit of the evolution of probability with respect to quantum stochastic processes.

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 A d S 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.

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.

The dynamics of a nearly-AdS₂ spacetime with boundaries is reduced to that of 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.

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.

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.