Infrared phases of 3D Class R theories

TL;DR

This paper investigates the infrared phases of 3D class R theories linked to non-hyperbolic 3-manifolds, revealing how topological properties influence IR phenomena like SUSY breaking and enhancement.

Contribution

It provides a detailed analysis of IR phenomena in 3D class R theories associated with non-hyperbolic 3-manifolds, highlighting the role of topological features in IR behavior.

Findings

Non-hyperbolic 3-manifolds lead to diverse IR phenomena such as SUSY breaking and mass gap generation.

Certain non-hyperbolic 3-manifolds always flow to 3D rank-0 $ abla$4 SCFTs with trivial moduli space.

Topological properties of 3-manifolds can predict IR phase characteristics.

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.