D3-instantons, Mock Theta Series and Twistors
arXiv:1207.1109 · doi:10.1007/JHEP04(2013)002
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,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.
42 pages; discussion of isometries is amended; misprints corrected
References in corpus (19)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Mock Theta Functions
- Wall-Crossing from Boltzmann Black Hole Halos
- String loop corrected hypermultiplet moduli spaces
- A Farey Tail for Attractor Black Holes
- Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
- D-instantons and twistors
- HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
- From AdS3/CFT2 to Black Holes/Topological Strings
- The chiral ring of AdS3/CFT2 and the attractor mechanism
- The M5-Brane Elliptic Genus: Modularity and BPS States
- Crossing the Wall: Branes vs. Bundles
- Quantum mirror symmetry and twistors
- Linear perturbations of Hyperkahler metrics
- Branes, Bundles and Attractors: Bogomolov and Beyond
- Membrane and fivebrane instantons from quaternionic geometry
- S-duality in Twistor Space
- On the topology of the hypermultiplet moduli space in type II/CY string vacua
- A 5d/2d/4d correspondence
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