Topological violation of global symmetries in quantum gravity

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.

19 pages. V2: references added; V3: minor improvement

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• Cosmic strings from pure Yang-Mills theory
• Asymptotic Observables and the Swampland
• Looking for structure in the cobordism conjecture
• Gravitational Solitons and Completeness
• Shining ALP Dark Radiation
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment