Free Energy from Replica Wormholes

TL;DR

This paper investigates how connected replica wormholes influence the free energy in certain gravity theories, revealing ensemble averaging and replica symmetry breaking phenomena that resemble spin glass behavior.

Contribution

It demonstrates that in JT gravity and simplified CGHS models, connected replica wormholes can dominate the free energy, indicating ensemble averaging and replica symmetry breaking in these theories.

Findings

Connected replica wormholes significantly affect free energy calculations.

Evidence of replica symmetry breaking similar to spin glasses.

Connected topologies can dominate over disconnected ones in certain regimes.

Abstract

Euclidean wormholes -- geometries which connect disconnected boundaries -- present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies, and appears in the computation of any extensive quantity. We argue that both JT gravity and a simplified version of CGHS admit a regime where the contribution of connected replica wormholes to the free energy is larger than that of disconnected topologies. In both theories we find evidence of replica symmetry breaking, which is reminiscent of the behavior of certain spin glasses. We discuss possible insights about ensemble averaging in gravity from this perspective.