Universal hypermultiplet metrics

TL;DR

This paper derives exact non-perturbative metrics for the universal hypermultiplet moduli space in type-IIA string theory, accounting for instanton effects from wrapped membranes and fivebranes, revealing new symmetric and flow solutions.

Contribution

It provides the first explicit non-perturbative hypermultiplet metrics for specific instanton configurations, expanding understanding of moduli space deformations in string theory.

Findings

Exact metrics for D-instantons without fivebranes

Exact metrics for fivebrane instantons with zero charges

Identification of symmetry-preserving and gradient flow solutions

Abstract

Some instanton corrections to the universal hypermultiplet moduli space metric of the type-IIA string theory compactified on a Calabi-Yau threefold arise due to multiple wrapping of BPS membranes and fivebranes around certain cycles of Calabi-Yau. The classical universal hypermultipet metric is locally equivalent to the Bergmann metric of the symmetric quaternionic space SU(2,1)/U(2), whereas its generic quaternionic deformations are governed by the integrable SU(infinity) Toda equation. We calculate the exact (non-perturbative) UH metrics in the special cases of (i) the D-instantons (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 preserve the U(1)xU(1) classical symmetry, while they can be interpreted as the gravitational dressing of the hyper-K"ahler D-instanton solutions. The second type solution preserves the non-abelian SU(2) classical symmetry, while it can be interpreted as a gradient flow in the universal hypermultiplet moduli space.