Description
I will discuss topological defect lines (TDLs) in 2d CFTs, that generate invertible and non-invertible symmetries. Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. I will present a classification of the rank-2 super fusion categories generalizing the Z8 classification for the anomalies of Z2 symmetry. Finally, I will discuss an interesting relation between q-type symmetries and fermionic symmetries.
