Non-invertible surface defects in 2+1d QFTs from half spacetime gauging

Abstract

Abstract We study duality defects in 2+1d theories with ℤ N 0 × ℤ N 1 $$ {\mathbb{Z}}_N^{(0)}\times {\mathbb{Z}}_N^{(1)} $$ 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, obtained from a four-dimensional BF theory gauging a ℤ N EM $$ {\mathbb{Z}}_N^{\textrm{EM}} $$ electric-magnetic symmetry. Furthermore, we provide explicit examples of such duality defects in U(1) × U(1) gauge theories and in more general product theories. Finally, we find duality defects in non-Lagrangian theories obtained by compactification of 6d N $$ \mathcal{N} $$ = (2, 0) SCFTs of type A N−1 on various three-manifolds.

Keywords

• Discrete Symmetries
• Global Symmetries
• Duality in Gauge Field Theories
• Wilson, ’t Hooft and Polyakov loops