Gauging noninvertible surface operators, and the 2-Deligne theorem.

Abstract: I will explain a generalization of the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. I will give examples of when we have reasonable control over these anomalies, and prove theorems about the structure of the 2-category obtained by condensing a suitable algebra object. I will provide examples where the resulting category displays grouplike fusion rules and through a cohomology computation, find the obstruction to condensing further to the vacuum theory. I will then present the main result of this work, which categorifies a theorem of Deligne about the existence of fibre functors for 1-categories. This work was done in collaboration with Thibault Decoppet.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.