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 \( \mathcal{N}=4\mathrm{U}{\left({N}_1\right)}_k\times \mathrm{U}{\left({N}_2\right)}_{-k} \) 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−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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Nosaka, T., Yokoyama, S. Index and duality of minimal \( \mathcal{N} = 4 \) Chern-Simons-matter theories. J. High Energ. Phys. 2018, 28 (2018). https://doi.org/10.1007/JHEP06(2018)028
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DOI: https://doi.org/10.1007/JHEP06(2018)028