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D3-instantons, mock theta series and twistors

  • Sergei Alexandrov
  • Jan Manschot
  • Boris Pioline
Open Access
Article

Abstract

The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2, \( \mathbb{Z} \)). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2, \( \mathbb{Z} \)) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.

Keywords

D-branes Differential and Algebraic Geometry Superstring Vacua String Duality 

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Copyright information

© SISSA 2013

Authors and Affiliations

  • Sergei Alexandrov
    • 1
  • Jan Manschot
    • 2
    • 3
  • Boris Pioline
    • 4
    • 5
  1. 1.Laboratoire Charles Coulomb, Universié Montpellier 2MontpellierFrance
  2. 2.Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  3. 3.Max Planck Institute for MathematicsBonnGermany
  4. 4.CERN PH-TH, Case C01600, CERNGeneva 23Switzerland
  5. 5.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Université Pierre et Marie CurieParis cedex 05France

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