Three-dimensional gauge theories with supersymmetry enhancement

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 the U(1) gauge group has the Chern-Simons level $\ensuremath{-}\frac{3}{2}$ 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 pieces of evidence for the conjecture: (i) exact match between the central charges of the U(1) R-symmetry current and the U(1) topological symmetry current, (ii) semiclassical construction of the $\mathcal{N}=4$ stress-tensor multiplet, and (iii) 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 $T[\mathrm{SU}(2)]$ theory, on the other. The duality in (iii) follows from geometrical aspects of the 3D--3D correspondence.