A JT/KPZ correspondence

TL;DR

This paper uncovers a deep connection between JT gravity and the KPZ equation's stationary measure, linking quantum gravity with stochastic growth processes through boundary conditions and correlation functions.

Contribution

It establishes a novel correspondence between JT gravity and KPZ, relating their measures and correlation functions via boundary conditions and limits.

Findings

JT gravity's path-integral measure matches KPZ stationary measure

Correlation functions are shown to correspond between the two frameworks

Relation between Schwarzian limit of SYK and weakly asymmetric limit of ASEP

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.