Refinement and modularity of immortal dyons

• Main Authors: Sergei Alexandrov, Suresh Nampuri
• Format: Article
• Language: English
• Published: SpringerOpen 2021-01-01
• Series: Journal of High Energy Physics
• Subjects: Black Holes in String Theory; Extended Supersymmetry; String Duality; Superstrings and Heterotic Strings
• Online Access: https://doi.org/10.1007/JHEP01(2021)147

Abstract Extending recent results in N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ of supersymmetries. We show that this equation allows to recover all known results about modularity (under SL(2, ℤ) duality group) of BPS states in N $$ \mathcal{N} $$ = 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.