2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging

Abstract

A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories ${\mathcal{C}}_G^{\times }$, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form $G$-symmetry on the neutral component ${\mathcal{C}}_e$ of ${\mathcal{C}}_G^{\times }$ produces its equivariantisation $({\mathcal{C}}_G^{\times }{)}^G$, which in turn features a generalised symmetry whose gauging recovers ${\mathcal{C}}_e$. If $G$ is commutative, the latter symmetry reduces to a 1-form symmetry involving the Pontryagin dual group.

63 pages