Signatures of global symmetry violation in relative entropies and replica wormholes

Understand

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.