Replica wormholes and capacity of entanglement

TL;DR

This paper investigates the capacity of entanglement as a diagnostic tool for Hawking radiation in a two-dimensional gravity model, revealing a potential discontinuity at the Page time and linking it to black hole thermal properties.

Contribution

It derives a formula for the capacity of entanglement using gravitational path integrals and applies it to replica wormholes, highlighting novel features at the Page time.

Findings

Capacity has a discontinuity at the Page time.

Capacity saturates the black hole's thermal capacity at high temperature.

Discontinuity contrasts with the continuous generalized entropy behavior.

Abstract

We consider the capacity of entanglement as a probe of the Hawking radiation in a two-dimensional dilaton gravity coupled with conformal matter of large degrees of freedom. A formula calculating the capacity is derived using the gravitational path integral, from which we speculate that the capacity has a discontinuity at the Page time in contrast to the continuous behavior of the generalized entropy. We apply the formula to a replica wormhole solution in an eternal AdS black hole coupled to a flat non-gravitating bath and show that the capacity of entanglement is saturated by the thermal capacity of the black hole in the high temperature limit.