Multiple D3-Instantons and Mock Modular Forms II View Full Text


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Article Info

DATE

2018-04

AUTHORS

Sergei Alexandrov, Sibasish Banerjee, Jan Manschot, Boris Pioline

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. More... »

PAGES

297-346

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-018-3114-z

DOI

http://dx.doi.org/10.1007/s00220-018-3114-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101406943


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41 schema:description 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.
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