3d dualities from 4d dualities for orthogonal groups

A bstract We extend recent work on the relation of 4 d and 3 d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO( N ) gauge theories in 4 d plays an important role in this relation. We show that the 4 d duality leads to a 3 d duality between an SO( N c ) gauge theory with N f flavors and an SO( N f − N c + 2) theory with N f flavors and extra singlets, and we derive its generalization in the presence of Chern-Simons terms. There are two different O ( N ) theories in 3 d , which we denote by O ( N ) ± , and we also show that the O ( N c ) − gauge theory is dual to a Spin( N f − N c + 2) theory, and derive from 4 d the known duality between O ( N c ) + and O ( N f − N c + 2) + . We verify the consistency of these 3 d dualities by various methods, including index computations.