Gauging Noninvertible Defects: A 2-Categorical Perspective

TL;DR

This paper develops a 2-categorical framework to understand noninvertible defects and anomalies in symmetries, providing new mathematical tools and examples for their classification and condensation behavior.

Contribution

It introduces a generalized notion of anomalies for noninvertible symmetries using condensation in 2-categories, with theorems on the structure after condensation and cohomology-based obstruction analysis.

Findings

Structured theorems on 2-category condensation

Examples with grouplike fusion rules

Cohomology computation of condensation obstructions

Abstract

We generalize the notion of an anomaly for a symmetry to a noninvertible symmetry enacted by surface operators using the framework of condensation in 2-categories. Given a multifusion 2-category, potentially with some additional levels of monoidality, we prove theorems about the structure of the 2-category obtained by condensing a suitable algebra object. We give examples where the resulting category displays grouplike fusion rules and through a cohomology computation, find the obstruction to condensing further to the vacuum theory.