Membrane Instantons and de Sitter Vacua

TL;DR

This work demonstrates that membrane instanton corrections in type IIA string theory on rigid Calabi–Yau threefolds deform the universal hypermultiplet’s quaternionic geometry in a controlled way described by the 3D Toda equation. By constructing explicit instanton solutions within the Przanowski–Tod framework and matching the resulting 4-fermion couplings to string theory predictions, the authors establish a consistent non-perturbative correction to the UH metric. When background fluxes are included, these instanton effects cooperate with the gauged supergravity potential to stabilize all hypermultiplet moduli and realize meta-stable de Sitter vacua, offering an alternative to KKLT-like constructions in IIA. The results point to a rich interplay between quaternion-Kähler geometry, Toda integrability, and non-perturbative string dynamics, and suggest avenues for extending the framework to include fivebrane instantons and additional moduli.

Abstract

We investigate membrane instanton effects in type IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. 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.