Abstract
We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a gauge theory of the local Lorentz group. By analogy, we deduce that gravity exhibits a one-form symmetry implemented by an operator Uα labeled by a center element α of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator Wρ is the holonomy in a spin representation ρ, which is the gravitational analog of a Wilson loop. The topological linking of Uα and Wρ has an elegant physical interpretation from classical gravitation: the former materializes an exotic chiral cosmic string defect whose quantized conical deficit angle is measured by the latter. We verify this claim explicitly in an AdS-Schwarzschild black hole background. Notably, our conclusions imply that the standard model exhibits a new symmetry of nature at scales below the lightest neutrino mass. More generally, the absence of global symmetries in quantum gravity suggests that the gravitational one-form symmetry is either gauged or explicitly broken. The latter mandates the existence of fermions. Finally, we comment on generalizations to magnetic higher-form or higher-group gravitational symmetries.
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Acknowledgments
We are very much grateful to Clay Córdova, Kurt Hinterbichler, Ted Jacobson, Mrunmay Jagadale, Austin Joyce, Anton Kapustin, Jake McNamara, Julio Parra-Martinez, Matthew Reece, and Shu-Heng Shao for many insightful discussions and detailed comments on our draft. C.C., M.D., J.-H.K., V.N., and N.S. are supported by the Department of Energy (Grant No. DE-SC0011632) and by the Walter Burke Institute for Theoretical Physics. J.-H.K. is also supported by Ilju Academy and Culture Foundation. I.Z.R. is supported by the Department of Energy (Grant No. DE-FG02-04ER41338 and FG02-06ER41449).
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Cheung, C., Derda, M., Kim, JH. et al. Generalized symmetry in dynamical gravity. J. High Energ. Phys. 2024, 7 (2024). https://doi.org/10.1007/JHEP10(2024)007
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DOI: https://doi.org/10.1007/JHEP10(2024)007