Signatures of global symmetry violation in relative entropies and replica wormholes

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 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.

Automated summary

Exact global symmetries are believed to not exist in theories with quantum black holes. This study proposes a method to quantify global symmetry violation in the Hawking radiation of a black hole using relative entropies. The violations of global symmetry considered are non-perturbative effects that contribute O(1) to relative entropy after the Page time, and these entropies can be computed within semi-classical gravity using island formulas.