Generalized Symmetry in Dynamical Gravity

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 $U_{\alpha }$ labeled by a center element $\alpha$ of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator $W_{\rho }$ is the holonomy in a spin representation $\rho$, which is the gravitational analog of a Wilson loop. The topological linking of $U_{\alpha }$ and $W_{\rho }$ 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.

Comments: 60 pages, 13 figures