Dyon Spectrum in CHL Models

TL;DR

This work extends the DVV framework for exact dyon degeneracies to CHL compactifications by introducing a genus-two modular form tildeΦ_k tied to the S-duality subgroup Γ1(N) and formulating d(Q) through the Fourier coefficients of 1/tildeΦ_k. The degeneracy depends only on the three T-duality invariants (Q_m^2/2, Q_e^2/2, Q_e·Q_m) and is computed via a three-variable integral over the genus-two period matrix, ensuring S-duality invariance and integrality. For large charges, the statistical entropy S_stat = ln d(Q) reproduces the extremal dyon black hole entropy to leading and first subleading order, including a φ(a,S) correction consistent with the CHL effective action. Altogether, the paper provides a duality-consistent, arithmetic counting formula for quarter BPS dyons in CHL models and strengthens the link between microscopic degeneracies and macroscopic black hole entropy.

Abstract

We propose a formula for the degeneracy of quarter BPS dyons in a class of CHL models. The formula uses a modular form of a subgroup of the genus two modular group Sp(2,Z). Our proposal is S-duality invariant and reproduces correctly the entropy of a dyonic black hole to first non-leading order for large values of the charges.