3d duality with adjoint matter from 4d duality

A bstract 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 S 1 -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.