Hypermultiplet metric and D-instantons

Abstract

We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kahler metric which is a non-trivial deformation of the local c-map. In the four-dimensional case corresponding to the universal hypermultiplet, our metric fits the Tod ansatz and provides an exact solution of the continuous Toda equation. We also analyze the fate of the curvature singularity of the perturbative metric by deriving an S-duality invariant equation which determines the singularity hypersurface after inclusion of the D(-1)-instanton effects.

arXiv comment20+12+4 pages

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• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
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• Mock modularity at work, or black holes in a forest
• Non-perturbative scalar potential inspired by type IIA strings on rigid CY
• Calabi-Yau compactification of type II string theories
• Lepton flavor violating top quark FCNC processes at the $\mu$TRISTAN