CHL Dyons and Statistical Entropy Function from D1-D5 System

TL;DR

This paper proves a formula for counting dyons in CHL string theories by relating it to D-brane configurations and develops a systematic method to compute their degeneracies using a duality-invariant entropy function.

Contribution

It provides a rigorous proof of the dyon spectrum formula in CHL models and introduces a systematic expansion method for degeneracy calculation.

Findings

Derived the locations of zeros and poles of Siegel modular forms.

Formulated the degeneracy computation as an extremization problem.

Validated the dyon spectrum formula through this mapping.

Abstract

We give a proof of the recently proposed formula for the dyon spectrum in CHL string theories by mapping it to a configuration of D1 and D5-branes and Kaluza-Klein monopole. We also give a prescription for computing the degeneracy as a systematic expansion in inverse powers of charges. The computation can be formulated as a problem of extremizing a duality invariant statistical entropy function whose value at the extremum gives the logarithm of the degeneracy. During this analysis we also determine the locations of the zeroes and poles of the Siegel modular forms whose inverse give the dyon partition function in the CHL models.