Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs

By applying the recently proposed (3D rank-0 N =4 SCFT)/(non-unitary TQFTs) correspondence to S-fold SCFTs, we construct an exotic class of non-unitary TQFTs labelled by an integer k =3. The SCFTs are obtained by gauging diagonal SU(2) subgroup of T[SU(2)] theory with Chern-Simons level k. We give the explicit expression for modular data, S and T matrices, of the TQFTs. When k = 4m(2) + 4m + 3 with an integer m = 1, the modular data (modulo a decoupled semion) is identical to a non-unitary Haagerup-Izumi modular data. Thus, we give a physical realization of the exotic non-unitary modular data as well as its generalization using an exotic class of SCFTs.