Defects and orbifolds in 3-dimensional TQFTs

Abstract

In this work we discuss defects and generalised orbifolds in 3-dimensional topological quantum field theories (TQFTs) of Reshetikhin-Turaev (RT) type. Generalised orbifolds provide one with a way to construct new TQFTs via a state-sum construction, internal to a fixed defect TQFT, i.e. having decorated stratified bordisms as the source category. The input needed for this procedure is called an orbifold datum. The main results of this work consist of constructing modular fusion categories out of orbifold data in the defect TQFTs of RT type and proving that the resulting generalised orbifolds are themselves TQFTs of RT type. We also explore several examples of modular fusion categories obtained this way, relating our approach to other constructions on modular fusion categories and demonstrating how it can be used to address some classification problems concerning them. Finally, we apply the above results to study surface defects separating two different theories of RT type.