Luisa Eck
Caltech
Title
Non-invertible symmetry enriched topological orders
Abstract
Topological orders enriched by group symmetries are well studied in both mathematics and physics, with symmetry twist defects described by G-crossed braided extensions. In this talk, I will outline a generalization to non-invertible symmetries. The starting point is a full inclusion of one fusion category into another, and the resulting twist defects are described by the relative center. I will explain how the symmetry action on anyons can be computed using tube algebra methods, and how it can send a single anyon to a sum of anyons and twist defects. The main example comes from Z2 inside S3, giving a non-invertible symmetry action on toric code anyons. The talk is based on upcoming work with Peter Huston, Kyle Kawagoe, and David Penneys.