Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold 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 $k\ge 3$. 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 $m\ge 1$, 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.

10 pages, v2: minor changes, typos corrected, v3: typos corrected and discussions clarified, v4: typos corrected

References in corpus (8)

• Notes on SUSY Gauge Theories on Three-Sphere
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Global Anomalies on the Hilbert Space
• Numerical evidence for a Haagerup conformal field theory
• A critical lattice model for a Haagerup conformal field theory
• M-theoretic Genesis of Topological Phases
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs

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• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models