Generalized symmetries and Noether’s theorem in $\mathrm{QFT}$

Benedetti, Valentin; Casini, Horacio; Magán, Javier M.

doi:10.1007/jhep08(2022)304

Generalized symmetries and Noether’s theorem in $$\mathrm{QFT}$$

Journal Article · Wed Aug 31 00:00:00 EDT 2022 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep08(2022)304· OSTI ID:1976527

Benedetti, Valentin ^[1]; Casini, Horacio ^[2]; Magán, Javier M. ^[3]

Instituto Balseiro, Centro Atómico Bariloche (Argentina); Univ. of Pennsylvania, Philadelphia, PA (United States)
Instituto Balseiro, Centro Atómico Bariloche (Argentina)
University of Pennsylvania, Philadelphia, PA (United States); Vrije Universiteit Brussel (VUB), Brussels (Belgium)

We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether’s theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten’s theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT’s with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity.

View Accepted Manuscript (DOE)

Research Organization:: University of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: CONICET; Simons Foundation; USDOE Office of Science (SC); Universidad Nacional de Cuyo

Grant/Contract Number:: SC0020360

OSTI ID:: 1976527

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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