Generalized Symmetry in Dynamical Gravity

TL;DR

This paper introduces a generalized one-form symmetry in dynamical gravity, linking gauge theory concepts to gravity via the tetrad formalism, and explores its physical implications and potential extensions.

Contribution

It transcribes known gauge theory results to gravity, revealing a new gravitational one-form symmetry and its physical interpretation, with implications for the standard model and quantum gravity.

Findings

Gravity exhibits a one-form symmetry analogous to gauge theories.

The symmetry is implemented by an operator related to cosmic string defects.

Implications include the necessity of fermions if the symmetry is broken or gauged.

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.