Three-dimensional gauge theories with supersymmetry enhancement

TL;DR

This paper proposes that certain three-dimensional  supersymmetric gauge theories exhibit emergent  supersymmetry in the infrared, supported by multiple independent evidences including symmetry matching, stress-tensor construction, and dualities.

Contribution

It provides the first nontrivial evidence for supersymmetry enhancement in 3d  gauge theories, connecting them to  theories via dualities and geometric insights.

Findings

Exact match of central charges for R-symmetry and topological symmetry.

Construction of  stress-tensor multiplet from  theory.

IR duality relating the  theory to an  theory via 3d-3d correspondence.

Abstract

We conjecture infrared emergent $\mathcal{N}=4$ supersymmetry for a class of three-dimensional $\mathcal{N}=2$ $U(1)$ gauge theories coupled with a single chiral multiplet. One example is the case where $U(1)$ gauge group has the Chern-Simons level $-\frac{3}2$ and the chiral multiplet has gauge charge $+1$. Other examples are related to this example either by known dualities or rescaling the Abelian gauge field. We give three independent evidences for the conjecture: 1) exact match between the central charges of the $U(1)$ R-symmetry current and the $U(1)$ topological symmetry current, 2) semi-classical construction of the $\mathcal{N}=4$ stress-tensor multiplet, and 3) an IR duality between a direct product of the two copies of the 3d theory on the one hand, and an $\mathcal{N}=4$ theory obtained by gauging the diagonal $SU(2)$ flavor symmetry of the $T[SU(2)]$ theory, on the other. The duality in 3) follows from geometrical aspects of the 3d-3d correspondence.