Superconformal index, BPS monodromy and chiral algebras

Abstract

We show that specializations of the 4d N= 2 superconformal index labeled by an integer N is given by Tr ℳN where ℳ is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras AN. This generalizes the recent results for the N = −1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S2× T2 where we turn on 12N units of U(1)r flux on S2.