Membrane and fivebrane instantons and quaternonic geometry

TL;DR

This paper studies membrane and fivebrane instanton effects in type IIA string theory on Calabi-Yau manifolds, revealing their impact on hypermultiplet geometry, moduli stabilization, and de Sitter vacua.

Contribution

It provides explicit instanton solutions, matches string theory predictions, and explores their role in moduli stabilization and metastable de Sitter vacua.

Findings

Membrane instantons are explicitly constructed and match string predictions.

Fivebrane instantons influence the hypermultiplet moduli space.

Membrane instantons contribute to moduli stabilization and de Sitter vacua.

Abstract

We investigate membrane and fivebrane instanton effects in type IIA string theory compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet, in four dimensional spacetime. To compute the nonperturbative effects due to the fivebrane instanton to the universal hypermultiplet, an instanton calculation is performed. In the absence of fivebrane instantons, the quaternionic geometry of the hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons and find perfect agreement with string theory predictions. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and the stabilization of moduli. Finally, we demonstrate the existence of meta-stable de Sitter vacua.