Twisted Theta Defects

Abstract

I will describe a uniform construction to gauge a discrete invertible symmetry S in possibly non-topological (D+1)-dimensional quantum systems with higher-categorical and possibly non-invertible symmetries. The symmetry in the theory obtained after gauging contains a sub-category of universal topological defects, which we term as Theta defects. These defects are universal in the sense that they exist in any system that can be obtained by gauging the symmetry S of some other system. These were discussed in last weeks seminar by Lakshya Bhardwaj and were shown to be equivalent to the D-category of lower (<= D dimensional) dimensional quantum systems with S-symmetry.I will focus on the non-universal symmetry defects within the gauged theory which are termed Twisted Theta defects. These correspond to an S-gauging of non-trivial defects in the pre-gauged theory stacked with lower (<= D dimensional) dimensional TQFTs. I will exemplify this construction by gauging invertible 0-form symmetries in quantum theories with 2-categorical symmetries in 2+1 dimensions. The 0-form groups I will discuss will be Z4, Z2 x Z2 and S3.