Topological violation of global symmetries in quantum gravity

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.

Automated summary

The paper discusses a topological reason why global symmetries are not conserved in quantum gravity, particularly when originating from compactification of a higher form symmetry. This mechanism is purely topological and does not necessitate any explicit breaking term in the UV Lagrangian. It is noted that local current conservation does not imply global charge conservation in a sum over geometries in the path integral.