D-instantons and twistors Auteur(s): Alexandrov S., Pioline Boris, Saueressig Frank, Vandoren Stefan (Article) Publié: Journal Of High Energy Physics, vol. p.044 (2009) Texte intégral en Openaccess : Ref HAL: hal-00349154_v1 Ref Arxiv: 0812.4219 DOI: 10.1088/1126-6708/2009/03/044 WoS: 000265600800044 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote 55 Citations Résumé: 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. |