Remarks on the locality of generalized global symmetries
Owen Gwilliam
TL;DR
The work asks how locality constrains generalized global symmetries and proposes a mathematical framework based on prefactorization algebras to capture nonperturbative, higher-degree symmetries. It shows that $q$-form symmetries are modeled by maps into Eilenberg–MacLane spaces, and generalizes to higher group symmetries via maps into arbitrary pointed spaces $Y$, with a Postnikov-tower perspective clarifying their layered structure. A key result is that $ ext{Map}_c(-,Y)$ forms a cosheaf for tailored Grothendieck topologies, yielding a higher nonabelian Poincaré duality-like structure, and enabling a Noether-like action of higher symmetries on observables through currents and bulk-boundary (SymTFT) formalisms. The paper lays groundwork for smooth refinements and anomaly theories as factorized central extensions, suggesting broad avenues to unify locality, symmetry, and nonperturbative QFT via factorization-algebraic methods.
Abstract
We examine generalized global symmetries as a kind of compactly supported cohomology, and so are led to revisit questions about the locality of quantum field theory, following Segal. Physics naturally suggests a generalization of factorization algebras, aimed at capturing nonperturbative information, and we explain how higher group symmetries offer examples of this generalization, providing an extension of the nonabelian Poincaré duality of Salvatore and Lurie. Finally, we explore how continuous generalized symmetries and anomalies can be cast in this framework.