Membrane Instantons and de Sitter Vacua

Abstract

We investigate membrane instanton effects in type IIA strings compactified on rigid CalabiYau 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.

Membrane and fivebrane instantons from quaternionic geometry

“…These results grew out of earlier work [16,17,11], see also [18 -21]. Recently, these instanton corrections also played a prominent role in the construction of meta-stable de Sitter vacua [14,22].…”

Inflation and String Theory

“…One problem with this modular picture, as we explain in detail in §4.2, is that geometric separation does not imply complete decoupling of two sectors. At the very least, the supersymmetry-breaking sector interacts with the remaining fields by its coupling to the overall compactification volume V: any source S of positive energy 33 in the four-dimensional theory must be negligible in the limit V → ∞, and so must enter the Lagrangian as [292,293,[401][402][403][404][405][406][407][408][409][410], while for proposals in the heterotic string, see [411][412][413][414][415]. See [416] for an early construction of de Sitter vacua in supercritical string theory, i.e.…”

Supergravity description of spacetime instantons

“…One way of writing the instanton action is [23] 14) with the same convention as for fivebranes, i.e. 15) and Q still defined by…”

“…Finally, we remark that instantons play an important role in the stabilization of moduli. For an example related to our discussion, we refer to [15]. This paper is organized as follows: In section 2 we treat NS-fivebrane instantons in the context of N = 1 supergravity.…”