On the distribution of stable de Sitter vacua

Abstract

The possible existence of (meta-) stable de Sitter vacua in string theory is of fundamental importance. So far, there are no fully stable solutions where all effects are under perturbative control. In this paper we investigate the presence of stable de Sitter vacua in type II string theory with non-geometric fluxes. We introduce a systematic method for solving the equations of motion at the origin of moduli space, by expressing the fluxes in terms of the supersymmetry breaking parameters. As a particular example, we revisit the geometric type IIA compactifications, and argue that non-geometric fluxes are necessary to have (isotropically) stable de Sitter solutions. We also analyse a class of type II compactifications with non-geometric fluxes, and study the distribution of (isotropically) stable de Sitter points in the parameter space. We do this through a random scan as well as through a complementary analysis of two-dimensional slices of the parameter space. We find that the (isotropically) stable de Sitter vacua are surprisingly rare, and organise themselves into thin sheets at small values of the cosmological constant.Comment: 24 pages, 8 figures, 2 tables; v3: references adde

Universal dS vacua in STU-models

“…The stable dS in [14][15][16][17] were all found to be close to Mkw vacua with no special properties. The aim of our work is to investigate the existence of examples close to either no-scale or fully supersymmetric Mkw.…”

“…Different theories are specified through various kinds of fluxes due to the metric and gauge fields living on the manifold. In order to find stable dS solution it has turned out to be crucial to turn on non-geometric fluxes, and explicit, successful examples can be found in refs [14][15][16][17].…”

“…In the context of isotropic STU-models, sets of stable dS critical points have been found both with pertubatively [14,16,17] and non-pertubatively [18,19] induced superpotentials. These critical points always turn out to be organised into thin regions in parameter space attached to a line of Mkw solutions.…”

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.…”

De Sitter vacua from a D-term generated racetrack uplift

“…Motivated by this setup, there were many attempts constructing dS vacua [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Using the necessary constraint for the extrema [43,44] and for the stability [45], we see that the existence of minima requires not only negative curvature, but also the presence of orientifold planes.…”