Non-invertible Symmetries and Higher Representation Theory

Abstract: There has recently been a lot of excitement surrounding non-invertible global symmetries and their potential applications. An important question is how to systematically construct theories whose non-invertible symmetry categories we can control well. In this talk I will suggest that higher representation theory can help us to answer this question when the symmetries are non-intrinsically non-invertible. In particular, I will explain how the topological defects obtained after gauging finite groups and 2-groups in 3 dimensions form the category of 2-representations of the original 2-group, and how this fact can be applied to some gauge theories with disconnected gauge groups. The same techniques can be extended to more general higher groups and subgroups in higher dimensions.

MathematicsPhysics

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.