Gauging Noninvertible Defects: A 2-Categorical Perspective
Category Theory
2023-04-03 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Algebra
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.
Cite
@article{arxiv.2211.08436,
title = {Gauging Noninvertible Defects: A 2-Categorical Perspective},
author = {Thibault D. Décoppet and Matthew Yu},
journal= {arXiv preprint arXiv:2211.08436},
year = {2023}
}
Comments
26 pages, v2 a new theorem about symmetric fusion 2-categories is added