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.

United States

Clifford Cheung

Maria Derda

Joon-Hwi Kim

Vinicius Nevoa

Ira Rothstein

Nabha Shah

Generalized symmetry in dynamical gravity

We derive a soft theorem for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.

CERN

Andreas Helset

Canada

Julio Parra-Martinez

Soft scalars in effective field theory

A variety of condensed matter systems describe gapless modes that can be interpreted as Nambu-Goldstone bosons of spontaneously broken Poincaré symmetry. In this paper we derive new soft theorems constraining the tree-level scattering of these degrees of freedom, as exhibited in solids, fluids, superfluids, and framids. These soft theorems are in one-to-one correspondence with various broken symmetries, including spacetime translations, Lorentz boosts, and, for the case of fluids, volume-preserving diffeomorphisms. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.

Soft phonon theorems