Gravitational dressing of D-instantons

TL;DR

This paper studies non-perturbative D-instanton effects on the hypermultiplet moduli space in type-IIA string theory, proposing a mechanism to construct quaternionic metrics from hyper-Kähler metrics with isometries, and analyzing solutions related to known gravitational instantons.

Contribution

It introduces a mechanism to derive quaternionic metrics from hyper-Kähler metrics with rotational isometry, connecting solutions to known gravitational instantons and D-instanton corrections.

Findings

Exact hypermultiplet metric governed by SU(∞) Toda equation.

Separable solutions relate to Eguchi-Hanson and Atiyah-Hitchin metrics.

Describes gravitational dressing of D-instantons.

Abstract

The non-perturbative corrections to the universal hypermultiplet moduli space metric in the type-IIA superstring compactification on a Calabi-Yau threefold are investigated in the presence of 4d, N=2 supergravity. These corrections come from multiple wrapping of the BPS (Euclidean) D2-branes around certain (BPS) Calabi-Yau 3-cycles, and they are known as the D-instantons. The exact universal hypermultiplet metric is governed by a quaternionic potential that satisfies the SU(\infty) Toda equation. The mechanism is proposed, which elevates any four-dimensional hyper-K"ahler metric with a rotational isometry to the quaternionic metric of the same dimension. A generic separable solution to the Toda equation appears to be related to the Eguchi-Hanson metric, whereas another solution originating from the Atiyah-Hitchin metric describes the gravitationally dressed (mixed) D-instantons.