Refinement and modularity of immortal dyons

Abstract

Extending recent results in $\mathcal{N}=2$ 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 $\mathcal{N}$ 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 $\mathcal{N}=4$ 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.

32 pages; references and clarifications added

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Cited by in corpus (2)

• Mock modularity at work, or black holes in a forest
• Modular anomaly of BPS black holes