3d duality with adjoint matter from 4d duality

TL;DR

This paper explores the relationship between 3d and 4d Seiberg dualities with adjoint matter in supersymmetric gauge theories, deriving 3d dualities from 4d ones via dimensional reduction and non-perturbative effects.

Contribution

It derives new 3d dualities with adjoint matter from known 4d dualities, including the Kim-Park and Aharony dualities, through dimensional reduction and non-perturbative analysis.

Findings

Derived 3d duality from 4d duality via compactification.

Connected Kim-Park duality with Aharony duality.

Extended dualities to $U(N)$ and $SU(N)$ gauge groups.

Abstract

We study the Seiberg dualities with an adjoint matter for the $U(N)$ and $SU(N)$ gauge groups in three- and four-dimensions with four supercharges. The relation between three- and four-dimensional dualities is investigated. We especially derive the three-dimensional duality from four-dimensional one by the dimensional reduction including the non-perturbative effect of the $\mathbb{S}^1$-compactification. In the $U(N)$ case, we obtain the Kim-Park duality, which is known as a generalization of the Aharony duality including an adjoint matter. In the $SU(N)$ case, we obtain the duality which follows from un-gauging the $U(N)$ Kim-Park duality.