Towards Classical de Sitter Solutions in String Theory

TL;DR

The paper tackles the existence of classical de Sitter solutions in Type II string theory with fluxes and orientifolds, presenting a tree-level framework and no-go analyses that reduce the problem to torsion-class conditions on SU(3)-structure manifolds. By deriving a universal 4D potential form and exploring smeared O6 configurations, the authors identify explicit torsion constraints on $W_1$ and $W_2$ that can support simple de Sitter solutions, test these in coset geometries and the Iwasawa manifold (finding none), and reveal new non-supersymmetric AdS vacua in certain cases. In the SU(3)-structure sector, degenerate flux configurations can yield de Sitter candidates within narrow parameter windows, but no fully explicit, backreaction-consistent dS geometry is presented. Overall, the work highlights the scarcity of perturbatively stable classical de Sitter vacua in this setting and outlines paths toward discovering explicit manifolds, including stability analyses and backreaction considerations.

Abstract

We investigate the type II string effective potential at tree-level and derive necessary ingredients for having de Sitter solutions in orientifold models with fluxes. Furthermore, we examine some explicit O6 compactifications in IIA supergravity on manifolds with SU(3)-structure in the limit where the orientifold sources are smeared. In particular, we use a simple ten-dimensional Ansatz for four-dimensional de Sitter solutions and find the explicit criteria in terms of the torsion classes such that these de Sitter solutions solve the equations of motion. We have verified these torsion conditions for the cosets and the Iwasawa manifold and it turns out that the conditions cannot be fulfilled for these spaces. However, this investigation allows us to find new non-supersymmetric AdS solutions for some cosets. It remains an open question whether there exist SU(3)-structure manifolds that satisfy the conditions on the torsion classes for these simple de Sitter solutions to exist.

Figures (1)

• Figure 1: $\left\vert W_{1}\right\vert ^{2}$ and $10^{-2}\times\left\vert W_{2}\right\vert ^{2}$ (dashed) as functions of $\beta$ when $F_4=0$.