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, 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.
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Alexandrov, S., Nampuri, S. Refinement and modularity of immortal dyons. J. High Energ. Phys. 2021, 147 (2021). https://doi.org/10.1007/JHEP01(2021)147
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DOI: https://doi.org/10.1007/JHEP01(2021)147