Quantum geometry of the universal hypermultiplet

TL;DR

This paper explores the non-perturbative geometry of the universal hypermultiplet moduli space in type-IIA string theory, linking it to integrable systems like Toda and Painleve VI equations, and calculating exact metrics for specific instanton cases.

Contribution

It provides exact non-perturbative metrics for the universal hypermultiplet moduli space using integrable systems, specifically relating instanton corrections to Toda and Painleve VI equations.

Findings

Exact metrics for D-instantons and fivebrane instantons derived

Connections established between string moduli space and integrable systems

Solutions characterized by Toda and Painleve VI equations

Abstract

The universal hypermultiplet moduli space metric in the type-IIA superstring theory compactified on a Calabi-Yau threefold is related to integrable systems. The instanton corrections in four dimensions arise due to multiple wrapping of BPS membranes and fivebranes around certain (supersymmetric) cycles of Calabi-Yau. The exact (non-perturbative) metrics can be calculated in the special cases of (i) the D-instantons (or the wrapped D2-branes) in the absence of fivebranes, and (ii) the fivebrane instantons with vanishing charges, in the absence of D-instantons. The solutions of the first type are governed by the three-dimensional Toda equation, whereas the solutions of the second type are governed by the particular Painleve VI equation.