The Classification of 3+1D Symmetry Enriched Topological Order

Abstract

We use a 2-categorical version of (de-)equivariantization to classify (3+1)d topological orders with a finite G-symmetry. In particular, we argue that (3+1)d fermionic topological orders with G-symmetry correspond to nondegenerate \(\textbf{2SVect}\)-central G-crossed braided fusion 2-categories. We then show that the categorical data necessary to define these theories agrees with that arising from a fermionic generalization of the Wang–Wen–Witten construction of bosonic topological theories with G-symmetry saturating an anomaly.