Topological violation of global symmetries in quantum gravity

TL;DR

This work identifies a purely topological mechanism by which global symmetries descending from compactified p-form symmetries are violated in quantum gravity, without explicit UV breaking terms. The authors show that summing over topologically distinct spacetimes can obstruct global charge conservation, implemented concretely through surgery that mimics virtual black branes and induces axion-like symmetry breaking. A key result is that the shift symmetry of axion-like fields, arising from p-form compactifications, acquires a potential via topological effects, with explicit demonstrations in a four-dimensional example where the path integral weight acquires a phase 2π i q φ. The findings illuminate how global symmetries fail in quantum gravity and suggest a controlled, topological route to symmetry breaking, with distinct implications for p>0 versus p=0 cases and potential connections to brane dynamics and holography.

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.