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

Abstract

Abstract We introduce a class of 3d theories consisting of strongly-coupled N $$ \mathcal{N} $$ = 4 systems coupled to N $$ \mathcal{N} $$ = 3 Chern-Simons gauge multiplets, which exhibit N $$ \mathcal{N} $$ = 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 T N theory, which enhances to N $$ \mathcal{N} $$ = 4 when 1/k 1 + 1/k 2 + 1/k 3 = 0. We also show that some but not all of these N $$ \mathcal{N} $$ = 4 enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of N $$ \mathcal{N} $$ = 4 theories which have not been studied previously.

Keywords

• Chern-Simons Theories
• Extended Supersymmetry
• String Duality
• Supersymmetry and Duality