Speaker
Description
Invertible symmetries are typically described by automorphisms and arise in groups. Non-invertible symmetries have also attracted much attention in quantum field theory in recent years. We review our work, joint with M. Bischoff and S. Del Vecchio, on non-invertible symmetries (also called quantum operations) in the special case of chiral conformal field theories, within the operator algebraic framework (AQFT).
Non-invertible symmetries in AQFT are described by families of unital completely positive (UCP) maps acting on the local algebras. We recall our motivation for studying them, their definition, and some general results. In the special case of rational conformal field theories, we show that fusion categories and certain double coset finite hypergroups describe our UCP actions. This provides a link with other descriptions of non-invertible symmetries in different contexts and frameworks, e.g., vertex operator algebras (VOAs).