3d duality with adjoint matter from 4d duality

We study the Seiberg dualities with an adjoint matter for the U(N) and the SU(N) gauge groups in three- and four-dimensions with four supercharges. The relation between three- and four-dimensional dualities is investigated. We derive the three-dimensional duality from four-dimensional one by the dimensional reduction including the non-perturbative effect of the S1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb{S}}^1 $$\end{document}-compactification. In the U(N) case, we obtain the Kim-Park duality which is known as a generalization of the Aharony duality to including an adjoint matter. In the SU(N) case, we obtain the duality which follows from un-gauging the U(N) Kim-Park duality.