Abstract

In this talk, I will discuss a class of “generalized tube algebras” which encode how topological line defects of 1+1d QFTs interact with junction operators, i.e. operators which sit at the intersection point of a collection of boundaries and interfaces. I will then describe how various aspects of the representation theory of these symmetry algebras can be studied using three-dimensional topological field theory techniques. With this machinery in hand, I will explain two different ways in which one can refine partition functions, focusing on the case of the annulus, so that they carry information about the action of a finite symmetry. The presentation will be organized around the derivation of a symmetry-resolved version of the Affleck-Ludwig-Cardy formula which, among other things, has applications to entanglement entropy.