Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N} =4$ CHL models

Abstract

We use continued fractions to perform a systematic and explicit characterization of the decays of two-centred dyonic black holes in $4D$ $\mathcal{N} =4$ heterotic $\mathbb{Z}_N$ CHL models. Thereby we give a new exact solution for the problem of counting decadent dyons in these models.