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.
Highlights
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 case of p = 0 and p > 0 are qualitatively different, and we will see that the situation seems to be much more transparent for pform symmetries with p > 0 without difficult conceptual issues such as baby universes and random couplings
We consider p-form U(1) global symmetries, the same conclusion holds for discrete p-form symmetries by more general characterization of symmetry operators as topological operators [20]
Summary
We would like to discuss why local current conservation does not imply global charge conservation in quantum gravity. Σt=−∞ and Σt=+∞ are topologically distinct on that manifold X In such a configuration, there is no reason at all that Q(Σt=−∞) and Q(Σt=+∞) should be the same. There is no reason at all that Q(Σt=−∞) and Q(Σt=+∞) should be the same This is the general reason that a charge is not expected to be conserved in quantum gravity. The results on JT gravity in [10] encourages us to consider gravitational contributions even if they do not satisfy equations of motion, that is, they are not saddle points of the path integral. It is reasonable to think that our configuration is relevant for the path integral
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