Free energy from replica wormholes

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.

Automated summary

The text discusses the challenge of Euclidean wormholes to the standard quantum mechanical interpretation and suggests that gravitational path integral computes the ensemble average of multiple theories. It highlights the contribution of connected topologies to the free energy and evidence of replica symmetry breaking in both JT gravity and a simplified version of CGHS. The insights about ensemble averaging in gravity from this perspective are also discussed.