Generalized symmetry in dynamical gravity - INSPIRE

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Generalized symmetry in dynamical gravity

Mar 4, 2024

60 pages

Published in:

JHEP 10 (2024) 007

Published: Oct 1, 2024

e-Print:

2403.01837 [hep-th]

DOI:

10.1007/JHEP10(2024)007

Report number:

CALT-TH 2024-009

View in:

ADS Abstract Service

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Abstract: (Springer)

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

_{α}

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 W

_{ρ}

is the holonomy in a spin representation ρ, which is the gravitational analog of a Wilson loop. The topological linking of U

_{α}

and W

_{ρ}

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.

Note:

60 pages, 13 figures

Global Symmetries
Wilson, ’t Hooft and Polyakov loops
Spacetime Singularities
group: Lorentz
cosmic string: chiral
spin: representation
symmetry: global
neutrino: mass
black hole: background
gravitation: classical

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