Dualities and flavored indices of M2-brane SCFTs

We study various conjectural dual descriptions of a stack of M2-branes in M-theory including ADHM, ABJ(M), BLG, discrete gauge theories and quiver Chern-Simons (CS) theories and propose several new dualities of the M2-brane SCFTs by analyzing flavored supersymmetric indices in detail. The mapping of local operators, Coulomb, Higgs and mixed branch operators as well as global symmetries under the dualities are obtained from the precise matching of the indices. Furthermore, we find closed form expressions for the Coulomb limit of the indices of the $U(N)$ ADHM theory and the dual quiver CS theory for arbitrary $N$ and propose a refined generating function for plane partitions with trace $N$. For the quiver CS theories we also find an infinite-sum expression for the Higgs limit of the indices which is more useful than the original expression.