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Journal of High Energy Physics, 03 (2009) 044
D-instantons and twistors
Sergey Alexandrov1, Boris Pioline2, Frank Saueressig3, Stefan Vandoren4

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds still poses an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instanton contributions are captured by contact transformations between different locally flat patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions. We conclude with some comments on the relation to microscopic degeneracies of four-dimensional BPS black holes and to the wall-crossing formula of Kontsevich and Soibelman, and on the form of the yet unknown NS5-brane instanton contributions.
1 :  LPTA - Laboratoire de Physique Théorique et Astroparticules
2 :  LPTHE - Laboratoire de Physique Théorique et Hautes Energies
3 :  IPHT - Institut de Physique Théorique (ex SPhT)
4 :  Institute for Theoretical Physics and Spinoza Institute
Physique/Physique des Hautes Energies - Théorie

Physique/Physique mathématique

Mathématiques/Physique mathématique
D-instantons – string theory – quaternionic geometry
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