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• W4237318530 abstract "We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action of S-duality on this moduli space: the generating function of DT invariants in the large volume attractor chamber must be a vector-valued mock modular form with specified modular properties. In this work, we prove that this condition is also sufficient at two-instanton order. This is achieved by producing a holomorphic action of SL(2,Z) on the twistor space which preserves the holomorphic contact structure. The key step is to cancel the anomalous modular variation of the Darboux coordinates by a local holomorphic contact transformation, which is generated by a suitable indefinite theta series. For this purpose we introduce a new family of theta series of signature (2,n-2), find their modular completion, and conjecture sufficient conditions for their convergence, which may be of independent mathematical interest." @default.
• W4237318530 created "2022-05-12" @default.
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• W4237318530 date "2018-03-10" @default.
• W4237318530 modified "2023-10-07" @default.
• W4237318530 title "Multiple D3-Instantons and Mock Modular Forms II" @default.
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• W4237318530 doi "https://doi.org/10.1007/s00220-018-3114-z" @default.
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