A JT/KPZ correspondence

TL;DR

This work exposes two deep dualities: a double-scaled SYK/ASEP correspondence and a JT/KPZ correspondence, linking a solvable quantum gravity setup to a non-equilibrium stochastic process. By aligning the DEHP algebra, chord-diagram transfer matrices, and Neumann boundary data, the authors show that the Euclidean evolution between end-of-the-world branes in JT gravity matches the stationary measure of open KPZ, while correlators align under the appropriate scaling limits. The key contributions include a concrete path-integral measure match, a mapping of brane tensions to KPZ boundary conditions, and a program to extend the correspondence to SUSY sectors, random-matrix frameworks, and higher-dimensional theories. The findings suggest a fundamental bridge between quantum gravity in two dimensions and non-equilibrium statistical mechanics, with potential implications for holography, matrix models, and integrable systems.

Abstract

We point out a correspondence between the Jackiw--Teitelboim (JT) gravity and the stationary measure of the Kardar--Parisi--Zhang (KPZ) equation on an interval. By relating the Schwarzian limit of the double-scaled SYK to the weakly asymmetric limit of the open ASEP, we establish that the path-integral measure defining the Euclidean evolution between two end-of-the-world branes in JT gravity can be interpreted as the stationary measure of the KPZ equation on an interval with Neumann boundary conditions. We also establish the match between correlation functions.

Figures (7)

• Figure 1: A schematic picture indicating the update rules of ASEP.
• Figure 2: (Left) A random walk update rule governing the evolution of the ASEP height function, with $n$ being an auxiliary coordinate. (Right) A reparametrisation of the left update rule using $\chi\equiv h-n$.
• Figure 3: ASEP phase diagram according to the stationary current $J$. The stationary current in the thermodynamic limit is also shown.
• Figure 4: A procedure of cutting open a chord diagram. The wiggly lines represent the slices on which the chord Hilbert space is defined.
• Figure 5: An interpretation of the chord Hilbert space. We start and end with a chord vacuum state corresponding to a maximally entangled state in the double-scaled SYK. The wiggly lines are slices on which our chord states are defined. They evolve according to the transfer matrices (represented as sites) acting on the left and the right Hilbert spaces, from/on which chords can emanate/close.