Global symmetry, Euclidean gravity, and the black hole information problem

TL;DR

This paper explores the deep link between the absence of global symmetries in quantum gravity and the unitarity of black hole evaporation, suggesting Euclidean quantum gravity may be equivalent to holography.

Contribution

It generalizes arguments against global symmetries in quantum gravity beyond AdS/CFT and connects these ideas to the black hole information paradox.

Findings

Recent Page curve calculations support the non-existence of global symmetries in quantum gravity.

Examples show some low-dimensional theories with global symmetries lack a unitary resolution of the information problem.

A conjecture links Euclidean quantum gravity to holography, implying a fundamental equivalence.

Abstract

In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.