Index and duality of minimal N=4 $$ \mathcal{N} = 4 $$ Chern-Simons-matter theories

Abstract

Abstract We perform a first step analysis toward generalization of the classification of N=4 $$ \mathcal{N} = 4 $$ linear quiver gauge theories by Gaiotto and Witten including Chern-Simons interaction. For this we investigate minimal N=4UN1k×UN2−k $$ \mathcal{N}=4\mathrm{U}{\left({N}_1\right)}_k\times \mathrm{U}{\left({N}_2\right)}_{-k} $$ Chern-Simons theories and their superconformal indices. In the previous publication we analyzed the three-sphere partition function of the theories, which implies that the theory is good/ugly/bad if k−N 1 −N 2 is greater than/equal to/smaller than −1. In this paper we verify that this classification is consistent with the behavior of the superconformal index. We compare the superconformal indices for several pairs of non-bad theories connected by the Hanany-Witten transition and confirm their coincidence up to the contribution of one hypermultiplet.

Keywords

• Chern-Simons Theories
• Duality in Gauge Field Theories
• Supersymmetric Gauge Theory