Speaker
Description
Non-invertible symmetries in general spacetime dimensions have attracted many attentions recently. I will present novel results for duality defects in 2+1 dimensional theories with $\mathbb{Z}^{(0)}_N\times\mathbb{Z}^{(1)}_N$ global symmetry and trivial mixed 't Hooft anomaly. By gauging these symmetries simultaneously in half of the spacetime, duality defects can be constructed for theories that are self-dual under gauging. The fusion rules involving duality defects form a fusion 2-category. I will also construct the corresponding symmetry topological field theory, a four-dimensional BF theory on a slab which realizes the duality defect on the boundary upon shrinking the interval. Furthermore, I will provide explicit examples of such duality defects in $U(1)\times U(1)$ gauge theories, in more general product theories and in non-Lagrangian theories obtained by compactification of 6d $\mathcal{N}=(2,0)$ SCFTs of type $A_{N-1}$ on various three-manifolds. Finally, I will discuss constraints on trivially gapped phases due to the existence of duality defects and a generalization of the above construction in five dimensions.
