Non-Invertible Surface Defects in 2+1d QFTs from Half Spacetime Gauging

Abstract

We study duality defects in 2+1d theories with $\bZ^{(0)}_N\times\bZ^{(1)}_N$ global symmetry and trivial mixed 't Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, we define duality defects for theories that are self-dual under gauging. We calculate the fusion rules involving duality defects and show that they obey a fusion 2-category. We also construct the corresponding symmetry topological field theory, a four-dimensional BF theory on a slab which realizes the duality defects on the boundary upon shrinking the interval. Furthermore, we provide explicit examples of such duality defects in $U(1)\times U(1)$ gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d $\cN=(2,0)$ SCFTs of type $A_{N-1}$ on various three-manifolds.