Constraints on non-invertible symmetries in 2+1D

Abstract: In this talk, I will discuss some constraints on non-invertible symmetries implemented by surface operators in 2+1D QFTs. I will first consider abelian TQFTs and argue that non-invertible surface operators exist if and only if there are bosonic line operators. I will then discuss an extension of this result to non-abelian TQFTs. This implies that all condensation defects are invertible in a TQFT without bosonic line operators. I will give an independent argument for this result using higher-gauging of line operators. Finally, I will discuss some implications for general 2+1D QFTs. This talk is based on the paper arxiv.org/abs/2309.15181 with Matthew Buican.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

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