  We show that specializations of the 4d $\mathcal{N}=2$ superconformal index
labeled by an integer $N$ is given by $\textrm{Tr}\,{\cal M}^N$ where ${\cal
M}$ 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 $\mathcal{A}_{N}$. 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 $S^2\times T^2$ where we turn
on $\frac{1}{2} N$ units of $U(1)_r$ flux on $S^2$.
