Generating Function of single-centered Black Hole Index in CHL Models

Abstract

We present the construction of the generating function of single-centered black hole index in general ${\mathbb{Z}}_N$ CHL models. This is done by subtracting from the index of quarter BPS dyons, described by a meromorphic Siegel modular form, the generating function for the index of two-centered black holes. We use black hole bound state metamorphosis in CHL models for the construction of the generating function of two-centered black hole index. We prove the convergence of the generating function for the cases $N=2,3$.

62 Pages, 7 Figures. Generalization of the generating function in arXiv:2510.05219 to CHL models. Proof of convergence follows the same steps as in arXiv:2510.05219.