Superconformal Index, BPS Monodromy and Chiral Algebras

Understand

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 $S^2$.