Infrared phases of 3D Class R theories

Abstract

We study the IR phases of 3D class R theories associated with closed non-hyperbolic 3-manifolds. Non-hyperbolic 3-manifolds can be obtained by performing Dehn fillings on 1-cusped hyperbolic 3-manifolds along exceptional slopes. In 3D-3D correspondence, the `exceptional' Dehn filling corresponds to the gauging of an $SU(2)$ flavor symmetry in a superconformal field theory associated with a 1-cusped 3-manifold with `small' Chern-Simons levels. With several explicit examples, we analyze various interesting non-perturbative IR phenomena (such as spontaneous SUSY breaking, generation of mass gap and supersymmetry enhancement) from the `exceptional' gaugings. Interestingly, distinguished features of the IR phases can be captured by simple topological properties of non-hyperbolic 3-manifolds. We also find that 3D class R theories associated with certain classes of atoroidal non-hyperbolic 3-manifolds always exhibit supersymmetry enhancement at low energy and actually flow to 3D rank-0 $\mathcal{N}=4$ SCFTs with trivial vacuum moduli space.

71 pages, 7 figures

References in corpus (5)

• Down the rabbit hole with theories of class S
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• From Three Dimensional Manifolds to Modular Tensor Categories
• From Torus Bundles to Particle-Hole Equivariantization

Cited by in corpus (4)

• On $\mathcal{N}=4$ supersymmetry enhancements in three dimensions
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• Resurgence in complex Chern-Simons theory at generic levels