Universal de Sitter solutions at tree-level

TL;DR

This paper explores universal de Sitter solutions in type IIA string theory compactified on SU(3)-structure manifolds, showing these solutions depend solely on universal geometric forms and torsion classes, simplifying their identification.

Contribution

It demonstrates the existence of a class of universal de Sitter solutions characterized by geometric conditions on SU(3)-structure manifolds, providing a purely geometric criterion for their existence.

Findings

Universal de Sitter solutions depend on SU(3)-structure forms and torsion classes.

Existence conditions are simple and geometrically verifiable.

The known SU(2)xSU(2) solution is an example of this class.

Abstract

Type IIA string theory compactified on SU(3)-structure manifolds with orientifolds allows for classical de Sitter solutions in four dimensions. In this paper we investigate these solutions from a ten-dimensional point of view. In particular, we demonstrate that there exists an attractive class of de Sitter solutions, whose geometry, fluxes and source terms can be entirely written in terms of the universal forms that are defined on all SU(3)-structure manifolds. These are the forms J and Omega, defining the SU(3)-structure itself, and the torsion classes. The existence of such universal de Sitter solutions is governed by easy-to-verify conditions on the SU(3)-structure, rendering the problem of finding dS solutions purely geometrical. We point out that the known (unstable) solution coming from the compactification on SU(2)x SU(2) is of this kind.