De Sitter hunting in a classical landscape

Abstract

We elaborate on the construction of de Sitter solutions from IIA orientifolds of SU(3)-structure manifolds that solve the 10-dimensional equations of motion at tree-level in the approximation of smeared sources. First we classify geometries that are orbifolds of a group manifold covering space which, upon the proper inclusion of O6 planes, can be described within the framework of N=1 supergravity in 4D. Then we scan systematically for de Sitter solutions, obtained as critical points of an effective 4D potential. Apart from finding many new solutions we emphasize the challenges in constructing explicit classical de Sitter vacua, which have sofar not been met. These challenges are interesting avenues for further research and include finding solutions that are perturbatively stable, satisfy charge and flux quantization, and have genuine localized (versus smeared) orientifold sources. This paper intends to be self-contained and pedagogical, and thus can serve as a guide to the necessary technical tools required for this line of research. In an appendix we explain how to study flux and charge quantization in the presence of a non-trivial H-field using twisted homology.Comment: 50 pages, 3 figure

Analytic classes of metastable de Sitter vacua

“…This is to be contrasted with the various earlier attempts to construct de Sitter vacua starting with specific string theory compactifications satisfying the relevant tadpole and quantization conditions, known as 'hunting for de Sitter vacua', see for example [22,41]. This direct approach did not have a significant rate of success since generically many more de Sitter solutions have been found which have tachyons.…”

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.…”

Universal dS vacua in STU-models

“…The natural models to study are the so called STU-models obtained through compactifying type IIB, type IIA (or M-theory) on twisted tori with orientifolds [7][8][9][10][11][12][13]. These models have an isotropic sector with three complex moduli (S, T and U ), while the full non-isotropic theory has 7 complex moduli.…”