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arXiv · 2009.01172

Refinement and modularity of immortal dyons

Sergei Alexandrov·Suresh Nampuri
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Abstract

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.

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Sergei Alexandrov, Suresh Nampuri. 2020-09-02. Refinement and modularity of immortal dyons. https://doi.org/10.1007/jhep01(2021)147

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