Generalized Symmetries, Noether currents and Gravitons

BENEDETTI VALENTIN; CASINI HORACIO; MAGAN JAVIER

Waterloo

Congreso; It from qubit 2023; 2023

Perimeter Institute for Theoretical Physics

We explain that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, if generalized symmetries are charged under such a continuous global symmetry, they must be generated by non-compact dual classes. In this context, we prove that a theory with an unbroken non-compact higher-form symmetry is necessarily massless and free. Therefore, these models cannot be completed in the UV without breaking the non-compact higher-form symmetry down to a compact one. This breaking requires the existence of charged operators appearing at a certain energy scale. We apply these ideas to gravity by showing how general theories of gravity exhibit emergent one-form symmetries in the IR that are charged under the Poincaré group. We use these results to rederive Weinberg-Witten’s theorem within local QFT, and we discuss the implications of these results in relation to the completeness principle in quantum gravity.