On the dyon partition function in N=2 theories

TL;DR

The paper extends entropy-function methods to two ${\cal N}=2$ theories (STU and FHSV) arising from freely acting ${\cal N}=4$ orbifolds, incorporating the Gauss–Bonnet higher-derivative correction to capture first subleading entropy for dyons. It derives exact attractor values for vector multiplet moduli and constructs duality-invariant dyon partition functions: a product of three weight-zero Siegel modular forms for STU that reproduces the subleading black-hole entropy, and an approximate weight-4 Siegel form-based partition function for FHSV in the regime of large electric charges. The results demonstrate that moduli dependences (axion–dilaton and T-moduli) enter the subleading corrections in a controlled way and confirm duality invariance, extending the exact matching between microscopic degeneracies and macroscopic entropy known in ${\cal N}=4$ to ${\cal N}=2$ theories. The work provides a concrete framework to compute and compare dyon degeneracies and entropy corrections in these ${\cal N}=2$ compactifications using Siegel modular forms and Gauss–Bonnet threshold data, with implications for understanding nonperturbative BPS spectra and black-hole physics in reduced supersymmetry settings.

Abstract

We study the entropy function of two N =2 string compactifications obtained as freely acting orbifolds of N=4 theories : the STU model and the FHSV model. The Gauss-Bonnet term for these compactifications is known precisely. We apply the entropy function formalism including the contribution of this four derivative term and evaluate the entropy of dyons to the first subleading order in charges for these models. We then propose a partition function involving the product of three Siegel modular forms of weight zero which reproduces the degeneracy of dyonic black holes in the STU model to the first subleading order in charges. The proposal is invariant under all the duality symmetries of the STU model. For the FHSV model we write down an approximate partition function involving a Siegel modular form of weight four which captures the entropy of dyons in the FHSV model in the limit when electric charges are much larger than magnetic charges.