3d dualities from 4d dualities

TL;DR

This paper explores the connection between four-dimensional and three-dimensional supersymmetric gauge theory dualities, showing how 4D dualities induce a variety of 3D dualities, including new ones, through dimensional reduction.

Contribution

It clarifies the relationship between 4D and 3D dualities and derives new 3D duals from known 4D dualities, especially for SU(N_c) supersymmetric QCD.

Findings

Every 4D duality induces a related 3D duality.

New duals for 3D SU(N_c) theories are derived from 4D dualities.

Many known and new 3D dualities are obtained through this approach.

Abstract

Many examples of low-energy dualities have been found in supersymmetric gauge theories with four supercharges, both in four and in three space-time dimensions. In these dualities, two theories that are different at high energies have the same low-energy limit. In this paper we clarify the relation between the dualities in four and in three dimensions. We show that every four dimensional duality gives rise to a three dimensional duality between theories that are similar, but not identical, to the dimensional reductions of the four dimensional dual gauge theories to three dimensions. From these specific three dimensional dualities one can flow to many other low-energy dualities, including known three dimensional dualities and many new ones. We discuss in detail the case of three dimensional SU(N_c) supersymmetric QCD theories, showing how to derive new duals for these theories from the four dimensional duality.