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arXiv · 0812.4219

D-instantons and twistors

Sergei Alexandrov·Boris Pioline·Frank Saueressig·Stefan Vandoren
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Abstract

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is 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 instantons are captured by contact transformations between different 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.

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Sergei Alexandrov, Boris Pioline, Frank Saueressig, Stefan Vandoren. 2008-12-22. D-instantons and twistors. https://doi.org/10.1088/1126-6708%2F2009%2F03%2F044

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