Signatures of global symmetry violation in relative entropies and replica wormholes

Y Chen, HW Lin�- Journal of High Energy Physics, 2021 - Springer
Journal of High Energy Physics, 2021Springer
A bstract 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�…
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(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.
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