Refinement and modularity of immortal dyons Auteur(s): Alexandrov S., Nampuri Suresh (Document sans référence bibliographique) 2020-09-02Texte intégral en Openaccess : Ref HAL: hal-02930775_v1 Ref Arxiv: 2009.01172 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: Extending recent results in ${\cal N}=2$ string compactifications, we propose that the holomorphic anomaly equation satisfied by the modular completions of the generating functions of refined BPS indices has a universal structure independent of the number ${\cal N}$ of supersymmetries. We show that this equation allows to recover all known results about modularity (under $SL(2,\mathbb{Z})$ duality group) of BPS states in ${\cal N}=4$ string theory. In particular, we reproduce the holomorphic anomaly characterizing the mock modular behavior of quarter-BPS dyons and generalize it to the case of non-trivial torsion invariant.