New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles

TL;DR

This paper explores new dualities in 3d $\\mathcal{N}=2$ gauge theories involving quadratic monopole superpotentials, using Hilbert series and partition functions to verify their validity.

Contribution

It introduces novel dualities with quadratic monopole superpotentials for various gauge groups, expanding the understanding of 3d $\\mathcal{N}=2$ dualities.

Findings

Proposes new dualities with quadratic monopole superpotentials.

Verifies dualities using Hilbert series and three-sphere partition functions.

Identifies obstructions to dualities with quartic monopole superpotentials.

Abstract

Aspects of three dimensional $\mathcal{N}=2$ gauge theories with monopole superpotentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new dualities involving quadratic powers for the monopole superpotentials, for unitary, symplectic and orthogonal gauge groups. These dualities are then tested using the three sphere partition function and matching of the Hilbert series. We also provide an argument for the obstruction to the duality for theories with quartic monopole superpotentials.