Topological violation of global symmetries in quantum gravity

TL;DR

This paper presents a topological explanation for why global symmetries are violated in quantum gravity, especially when originating from higher form symmetries, without requiring explicit symmetry-breaking terms.

Contribution

It introduces a purely topological mechanism demonstrating the non-conservation of global symmetries in quantum gravity, linked to compactified higher form symmetries and spacetime topology.

Findings

Global symmetries from compactified higher forms are topologically violated in quantum gravity.

Local current conservation does not guarantee global charge conservation in the path integral.

The mechanism is motivated by brane/black-brane correspondence and spacetime surgery ideas.

Abstract

We discuss a topological reason why global symmetries are not conserved in quantum gravity, at least when the symmetry comes from compactification of a higher form symmetry. The mechanism is purely topological and does not require any explicit breaking term in the UV Lagrangian. Local current conservation does not imply global charge conservation in a sum over geometries in the path integral. We explicitly consider the shift symmetry of an axion-like field which originates from the compactification of a $p$-form gauge field. Our topological construction is motivated by the brane/black-brane correspondence, brane instantons, and an idea that virtual black branes of a simple kind may be realized by surgery on spacetime manifolds.