Smooth generalized symmetries of quantum field theories

Abstract: In this talk, based on joint work with Ben Gripaios and Oscar Randal-Williams (arXiv:2209.13524 and 2310.16090), we will, with help from the geometric cobordism hypothesis, define and study invertible smooth generalized symmetries of field theories within the framework of higher category theory. We will show the existence of a new type of anomaly that afflicts global symmetries even before trying to gauge, we call these anomalies “smoothness anomalies”. In addition, we will see that d-dimensional QFTs when considered collectively can have d-form symmetries, which goes beyond the (d-1)-form symmetries known to physicists for individual QFTs. We will also touch on aspects of gauging global symmetries in the case of topological quantum field theories.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

( paper )

Topology and Geometry Seminar (Texas, Kansas)