Index and duality of minimal N=4 Chern-Simons-matter theories

TL;DR

This paper explores the classification and dualities of minimal N=4 Chern-Simons-matter theories, analyzing their superconformal indices to verify consistency with previous partition function results and Hanany-Witten transitions.

Contribution

It extends the classification of N=4 linear quiver gauge theories to include Chern-Simons interactions and verifies index behavior under dualities.

Findings

Superconformal index matches the three-sphere partition function classification.

Indices for dual theories connected by Hanany-Witten transition coincide.

The classification of theories as good, ugly, or bad is consistent with index analysis.

Abstract

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.