Global symmetry violation from non-isometric codes

TL;DR

This paper models black holes as non-isometric codes to explore the violation of global symmetries in quantum gravity, providing quantitative measures and discussing implications for black hole remnants.

Contribution

It introduces a model of black holes as non-isometric codes to demonstrate and quantify global symmetry violation in quantum gravity.

Findings

States with different charges have non-zero overlaps due to non-isometric maps.

Renyi entropies of radiation align with the quantum extremal surface formula.

Global symmetries are demonstrated to be violated in Hawking radiation.

Abstract

We study the no-global-symmetry conjecture in quantum gravity by modeling black holes as non-isometric codes that encode the interior states with global charges into the fundamental states. The fluctuation in the inner products of the charged states can be larger compared to the case without charges. The non-isometric map causes states with different charges to have non-zero overlaps, signaling symmetry violation. The Renyi entropies of the radiation with global charges are found to be consistent with the quantum extremal surface formula. We compute various forms of Renyi relative entropy, as well as the fidelity, to quantify the degree of a global symmetry violation in Hawking radiation, demonstrating that global symmetries are indeed violated. We also comment on the instability of the black hole remnant.