A tour of categorical symmetry

I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.

This talk is based on https://arxiv.org/abs/1912.02817 , https://arxiv.org/abs/2003.04328 , and https://arxiv.org/abs/2106.12577