On $$ \mathcal{N} $$ = 4 supersymmetry enhancements in three dimensions

Abstract

Abstract We introduce a class of 3d theories consisting of strongly-coupled $$ \mathcal{N} $$ N = 4 systems coupled to $$ \mathcal{N} $$ N = 3 Chern-Simons gauge multiplets, which exhibit $$ \mathcal{N} $$ N = 4 enhancements when a peculiar condition on the Chern-Simons levels is met. An example is the SU(N)3 Chern-Simons theory coupled to the 3d TN theory, which enhances to $$ \mathcal{N} $$ N = 4 when 1/k1 + 1/k2 + 1/k3 = 0. We also show that some but not all of these $$ \mathcal{N} $$ N = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of $$ \mathcal{N} $$ N = 4 theories which have not been studied previously.