Signatures of global symmetry violation in relative entropies and replica wormholes

TL;DR

This paper introduces a method to quantify global symmetry violations in black hole Hawking radiation using relative entropies, revealing non-perturbative effects that become significant after the Page time and are computable via semi-classical gravity and replica tricks.

Contribution

It proposes a novel approach to measure global symmetry violation in black hole radiation through relative entropies, connecting non-perturbative effects with replica wormholes and island formulas.

Findings

Global symmetry violations contribute order-one effects after the Page time.

Relative entropies can be computed using island formulas in semi-classical gravity.

Charge flow through replica wormholes indicates symmetry violation effects.

Abstract

It is widely believed that exact global symmetries do not exist in theories that admit quantum black holes. Here we propose a way to quantify the degree of global symmetry violation in the Hawking radiation of a black hole by using certain relative entropies. While the violations of global symmetry that we consider are non-perturbative effects, they nevertheless give $\mathcal{O}(1)$ contributions to the relative entropy after the Page time. Furthermore, using "island" formulas, these relative entropies can be computed within semi-classical gravity, which we demonstrate with explicit examples. These formulas give a rather precise operational sense to the statement that a global charge thrown into an old black hole will be lost after a scrambling time. The relative entropies considered here may also be computed using a replica trick. At integer replica index, the global symmetry violating effects manifest themselves as charge flowing through the replica wormhole.