%0 Journal Article
%T Multiple D3-Instantons and Mock Modular Forms II
%+ Laboratoire Charles Coulomb (L2C)
%A Alexandrov, Sergey
%A Banerjee, Sibasish
%A Manschot, Jan
%A Pioline, Boris
%Z 24+24 pages
%< avec comité de lecture
%Z L2C:17-011
%@ 0010-3616
%J Communications in Mathematical Physics
%I Springer Verlag
%V 359
%N 1
%P 297-346
%8 2018-04
%D 2018
%Z 1702.05497
%R 10.1007/s00220-018-3114-z
%Z Physics [physics]/High Energy Physics - Theory [hep-th]
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Algebraic Geometry [math.AG]
%Z Mathematics [math]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Number Theory [math.NT]Journal articles
%X 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.
%G English
%L hal-01627846
%U https://hal.science/hal-01627846
%~ CNRS
%~ LPTHE
%~ L2C
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ SU-TI
%~ ALLIANCE-SU
%~ UM-2015-2021