%0 Journal Article
%T D3-instantons, Mock Theta Series and Twistors
%+ Laboratoire Charles Coulomb (L2C)
%+ Max Planck Institute for Mathematics (MPIM)
%+ Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
%A Alexandrov, Sergey
%A Manschot, Jan
%A Pioline, Boris
%Z 42 pages
%< avec comité de lecture
%Z L2C:12-090
%@ 1126-6708
%J Journal of High Energy Physics
%I Springer
%P 002
%8 2013-04-02
%D 2013
%Z 1207.1109
%R 10.1007/JHEP04(2013)002
%Z Physics [physics]/High Energy Physics - Theory [hep-th]
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Mathematical Physics [math-ph]Journal articles
%X 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,Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,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.
%G English
%2 https://hal.science/hal-00715152/document
%2 https://hal.science/hal-00715152/file/Alexandrov2013_Article_D3-instantonsMockThetaSeriesAn.pdf
%L hal-00715152
%U https://hal.science/hal-00715152
%~ UNIV-PARIS7
%~ UPMC
%~ CNRS
%~ LPTHE
%~ L2C
%~ TDS-MACS
%~ UPMC_POLE_2
%~ MIPS
%~ UNIV-MONTPELLIER
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ UNIV-PARIS
%~ SU-TI
%~ ALLIANCE-SU
%~ UM-2015-2021