Generalized symmetries of topological field theories

TL;DR

This paper explores generalized symmetries in topological field theories using homotopy theory, providing new insights into global and gauge symmetries and their anomalies.

Contribution

It introduces a homotopy-theoretic framework to analyze generalized symmetries and anomalies in topological field theories, bridging a gap in understanding beyond traditional quantum field theories.

Findings

Classified 't Hooft anomalies into two types

Provided a homotopy-theoretic approach to symmetries in topological theories

Connected earlier symmetry work with new topological insights

Abstract

We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of homotopy theory. We study both global and gauge symmetries, as well as `t Hooft anomalies, which we show fall into one of two classes. Our approach also allows some insight into earlier work on symmetries (generalized or not) of topological field theories.