A Tale of Two Saddles

TL;DR

This paper discovers a new stable saddle in JT gravity with matter, which influences the classical generating functional and may be stabilized by quantum corrections, revealing signature-dependent behavior.

Contribution

It introduces a novel on-shell replica wormhole saddle in JT gravity, including a construction for its on-shell action and analysis of stability under different signatures.

Findings

New on-shell replica wormhole saddle found in JT gravity.

The saddle has lower action than disconnected solutions.

Quantum corrections may stabilize the new saddle.

Abstract

We find a new on-shell replica wormhole in a computation of the generating functional of JT gravity coupled to matter. We show that this saddle has lower action than the disconnected one, and that it is stable under restriction to real Lorentzian sections, but can be unstable otherwise. The behavior of the classical generating functional thus may be strongly dependent on the signature of allowed perturbations. As part of our analysis, we give an LM-style construction for computing the on-shell action of replicated manifolds even as the number of boundaries approaches zero, including a type of one-step replica symmetry breaking that is necessary to capture the contribution of the new saddle. Our results are robust against quantum corrections; in fact, we find evidence that such corrections may sometimes stabilize this new saddle.