Confinement for 3d $\mathcal{N}=2$ $SU(N)$ with a Symmetric tensor

Abstract: In this paper we study 3d $\mathcal{N}=2$ $SU(N)$ confining gauge theories with a matter field in the rank-two index symmetric representation. The models found here are obtained from the application of the duplication formula for hyperbolic gamma functions from \emph{parent} confining models, with antisymmetric fields and (anti)-fundamental matter by \emph{freezing} some of the mass parameters for the latter. We find a series of identities that can give rise to candidate confining theories with $SU(N)$ gauge group, a symmetric tensor and in addition other charged matter fields, in general with a non-vanishing superpotential. We provide for each case further checks of the proposed dualities, by studying the Coulomb branch and by deconfining the tensorial matter by using other known 3d dualities. From the final picture a refined classification emerges, distinguishing the confining theories obtained in the paper in classes with common properties.