Symplectic Chern-Simons theories dual to Abelian rank-$0$ theories

Abstract

We propose that the 3d symplectic Chern-Simons theory $USp(2n)$ at level $k=n+\frac12+\ell$ with a single chiral multiplet in the fundamental representation is dual, for every pair of positive integers $(n,\ell)$, to the Abelian rank-$0$ theory $\mathcal{T}_{\ell,n}$ of Creutzig, Garner and Kim. The fundamental is pseudo-real, so the level is half-integral, there is no non-Abelian flavor symmetry, and the supersymmetry is enhanced to $\mathcal{N}=4$. Both sides have vanishing Higgs and Coulomb branches. We match the counting of supersymmetric vacua under real mass deformations for all $(n,\ell)$, and the supersymmetric indices in a number of cases. We then study in detail the case $\ell=1$, the minimal $USp(2n)$ Chern-Simons theory at level $n+\frac32$, whose dual is a $U(1)^{n}$ theory with a tadpole level matrix and a bare monopole superpotential.