Abstract
We perform a first step analysis toward generalization of the classification of mathcal{N} = 4 linear quiver gauge theories by Gaiotto and Witten including Chern-Simons interaction. For this we investigate minimal mathcal{N}=4mathrm{U}{left({N}_1right)}_ktimes mathrm{U}{left({N}_2right)}_{-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−N1 −N2 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.
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