Non-invertible Defects from Higher Gauging

Sahand Seifnashri

I discuss invertible and non-invertible topological condensation defects arising from gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime, which we define as higher gauging. A q-form symmetry is called p-gaugeable if it can be gauged on a codimension-p manifold in spacetime. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFTs, and gauge them on a surface in spacetime. The universal fusion rules of the resulting invertible and non-invertible condensation surfaces are determined. We emphasize that the fusion “coefficients” in these non-invertible fusion rules are generally not numbers, but rather 1+1d TQFTs. In the special case of 2+1d TQFT, every (invertible and noninvertible) 0-form global symmetry, including the Z2 electromagnetic symmetry of the Z2 gauge theory, is realized from higher gauging. Finally, we discuss examples of non-invertible symmetries in non-topological 2+1d QFTs.

http://scgp.stonybrook.edu/video_portal/video.php?id=5159

Simons- Program: Geometrical aspects of topological phases of matter: spatial symmetries, fractons and beyond