Finite-cutoff JT gravity and self-avoiding loops

TL;DR

This paper explores quantum JT gravity at finite cutoff by mapping it to the statistical mechanics of self-avoiding loops in hyperbolic space, analyzing different regimes of loop sizes and their quantum behavior.

Contribution

It introduces a novel mapping between finite-cutoff JT gravity and self-avoiding loop models, providing insights into quantum effects across various loop size regimes.

Findings

Semiclassical effective description valid for intermediate loop sizes

Quantum regime for large loops governed by Schwarzian theory

Small loops analyzed using self-avoiding walk conjecture

Abstract

We study quantum JT gravity at finite cutoff using a mapping to the statistical mechanics of a self-avoiding loop in hyperbolic space, with positive pressure and fixed length. The semiclassical limit (small $G_N$) corresponds to large pressure, and we solve the problem in that limit in three overlapping regimes that apply for different loop sizes. For intermediate loop sizes, a semiclassical effective description is valid, but for very large or very small loops, fluctuations dominate. For large loops, this quantum regime is controlled by the Schwarzian theory. For small loops, the effective description fails altogether, but the problem is controlled using a conjecture from the theory of self-avoiding walks.