Non-Invertible Symmetries, Boundary Conditions, and Topological Field Theory

In recent years, there have been various activities trying to better understand the interplay between non-invertible global symmetries and boundary conditions in quantum field theories, with applications ranging from scattering of solitons to symmetry-resolved entanglement entropies. In this talk, I will focus on 1+1d conformal field theories, and start by reviewing some of the fundamental properties of topological line defects that generate global symmetries. I will then discuss how the algebra of symmetry operators is modified in the presence of conformal boundary conditions. Universal kinematic aspects of this symmetry algebra, such as its representation theory, are neatly captured by a 2+1d topological field theory defined on manifolds with corners, which I will explain.

Based on https://arxiv.org/pdf/2409.02159 and https://arxiv.org/pdf/2409.02806.