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.

arXiv comment71 pages, 7 figures

References in corpus (30)

• N=2 dualities
• The Exact Superconformal R-Symmetry Extremizes Z
• SUSY Gauge Theories on Squashed Three-Spheres
• Quantum Dilogarithm
• Vortex Counting and Lagrangian 3-manifolds
• A topologically twisted index for three-dimensional supersymmetric theories
• Index for three dimensional superconformal field theories with general R-charge assignments
• Holomorphic Blocks in Three Dimensions
• Comments on twisted indices in 3d supersymmetric gauge theories
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Down the rabbit hole with theories of class S
• Supersymmetric partition functions and the three-dimensional A-twist
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Supersymmetric vacua of mass-deformed M2-brane theory
• Three-dimensional gauge theories with supersymmetry enhancement
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs
• M-theoretic Genesis of Topological Phases
• 3d-3d Correspondence Revisited
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
• A 3d-3d appetizer
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• From Three Dimensional Manifolds to Modular Tensor Categories
• From Torus Bundles to Particle-Hole Equivariantization
• Quantum Approach to Dehn Surgery Problem

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