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

TL;DR

This paper constructs a new class of non-unitary topological quantum field theories from 3D SCFTs, explicitly deriving their modular data and connecting them to exotic non-unitary modular data like the Haagerup-Izumi type.

Contribution

It introduces a novel construction of non-unitary TQFTs from 3D SCFTs and provides explicit modular data, linking physical theories to exotic non-unitary modular data.

Findings

Explicit modular S and T matrices for the constructed TQFTs.

Identification of cases where modular data matches non-unitary Haagerup-Izumi data.

Physical realization of exotic non-unitary modular data using SCFTs.

Abstract

By applying the recently proposed (3D rank-0 $\mathcal{N}$=4 SCFT)/(non-unitary TQFTs) correspondence to S-fold SCFTs, we construct an exotic class of non-unitary TQFTs labelled by an integer $k\geq 3$. 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 $m\geq 1$, 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.