Non-unitary Haagerup-like TQFTs and RCFTs from generalized S-fold SCFTs

Building on earlier work by Gang, Kim, and Lee, we extend the known class of 3-dimensional non-unitary topological quantum field theories (TQFTs) and 2-dimensional non-unitary rational conformal field theories (RCFTs). The TQFTs are obtained by applying topological twist to generalized S-fold superconformal field theories (SCFTs). They are related to the RCFTs through the bulk-boundary correspondence. For certain families, we propose simple lines in the TQFTs, together with expressions for the characters and modular $S$ matrices of their associated boundary RCFTs. For broader family, we propose modular $S$ and $T$ matrices for the TQFTs. For particular members of this family, the resulting modular matrices are identified with the generalized Haagerup-Izumi modular matrices up to Galois conjugation.