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

TL;DR

This paper explores 3d $ ext{N}=2$ $SU(N)$ confining gauge theories with symmetric tensor matter, deriving new dualities and identities through hyperbolic gamma function formulas, and classifying the resulting theories.

Contribution

It introduces new confining dualities for 3d $ ext{N}=2$ $SU(N)$ theories with symmetric tensors, expanding the understanding of their dualities and matter content.

Findings

Derived identities from hyperbolic gamma functions leading to confining theories.

Proposed dualities for theories with symmetric tensor and additional matter fields.

Classified confining theories into distinct classes based on properties.

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.