Hypermultiplet metric and D-instantons

TL;DR

This paper derives an explicit quaternion-Kahler metric for hypermultiplet moduli space in Calabi-Yau compactifications, incorporating D-instanton effects and analyzing the impact on singularities, using twistorial methods.

Contribution

It provides the first explicit construction of the hypermultiplet metric including D-instanton corrections via twistorial techniques, extending the local c-map.

Findings

Derived an exact quaternion-Kahler metric with D-instanton corrections.

Fitted the universal hypermultiplet metric into the Tod ansatz, solving the Toda equation.

Analyzed the curvature singularity, deriving an S-duality invariant condition for its resolution.

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.