On Classical de Sitter Vacua in String Theory

TL;DR

This work surveys the prospects for classical, tree-level de Sitter vacua in closed-string compactifications without NSNS sources, focusing on two controlled 4D N=1 setups: IIA on SU(3)-structure manifolds with O6-planes and IIB on SU(2)-structure manifolds with O5/O7-planes. It analyzes no-go theorems in the volume-dilaton plane and shows how negative curvature or specific flux/orientifold combinations can evade the bounds, but fully stable dS vacua remain elusive, with AdS vacua being more readily realized. In IIA, refined no-go arguments exclude most coset and twisted-torus models, leaving a pair of spaces with dS points that are tachyonic; in IIB, AdS vacua with large volume are achievable, while dS solutions generally carry tachyonic instabilities, with a single evading case tied to SU(2)×SU(2) with O5/O7. The results delineate landscape boundaries for classical dS realizations and stress the need for non-geometric fluxes or quantum corrections to achieve robust, stable de Sitter vacua.

Abstract

We review the prospect of obtaining tree-level de Sitter (dS) vacua and slow-roll inflation models in string compactifications. Restricting ourselves to the closed string sector and assuming the absence of NSNS-sources, we classify the minimal classical ingredients that evade the simplest no-go theorems against dS vacua and inflation. Spaces with negative integrated curvature together with certain combinations of low-dimensional orientifold planes and low-rank RR-fluxes emerge as the most promising setups of this analysis. We focus on two well-controlled classes that lead to an effective 4D, N=1 supergravity description: Type IIA theory on group or coset manifolds with SU(3)-structure and O6-planes, as well as type IIB compactifications on SU(2)-structure manifolds with O5- and O7-planes. While fully stabilized AdS vacua are generically possible, a number of problems encountered in the search for dS vacua are discussed.