Abstract

We investigate the modularity constraints on the generating series $h_r(\tau)$ of BPS indices counting D4-D2-D0 bound states with fixed D4-brane charge $r$ in type IIA string theory compactified on complete Intersection Calabi-Yau threefolds with $b_2 = 1$. For unit D4-brane, $h_1$ transforms as a (vector-valued) modular form under the action
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