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

We perform a first step analysis toward generalization of the classification of N=4 linear quiver gauge theories by Gaiotto and Witten including Chern-Simons interaction. For this we investigate minimal N=4 U(N_1)_k x U(N_2)_{-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.