On 3d Seiberg-like Dualities with Two Adjoints

TL;DR

This paper explores three-dimensional N=2 theories with two adjoint fields and specific superpotentials, proposing dualities derived from four-dimensional theories, and confirms these dualities through index factorization and vortex partition functions.

Contribution

It introduces new 3d dualities for theories with two adjoints and D-type superpotentials, supported by detailed index and vortex partition function analysis.

Findings

Precise matching of vortex partition functions between dual theories

Identification of discrete Higgs vacua contributing to vortex partition functions

Clarification of monopole operators parametrizing the Coulomb branch

Abstract

We study $N = 2$ 3-d theories with two adjoints and fundamental flavors along with D-type superpotential. For superpotential $W_{D_{n+2}} = \mathrm{Tr} \left(X^{n+1}+X Y^2\right)$ with $n$ odd, we propose the 3d dualities, which we motivate from the dimensional reduction of the related 4-d theory. We consider the factorization of the superconformal index and match precisely the vortex partition function of the dual pairs. In the language of the Higgs branch localization, the nonzero contribution of the vortex partition function comes from the discrete Higgs vacua of the massively deformed theory, which precisely matches with that of the dual theory. We also clarify the monopole operators parametrizing the Coulomb branch of such theories. Existence of independent monopole operators of charge 2 is crucial to describe the Coulomb branch.