Universal de Sitter solutions at tree-level

TL;DR

The paper proves the existence of a universal class of tree-level de Sitter solutions in Type IIA flux compactifications on SU(3)-structure manifolds with O6-planes, expressible entirely through universal forms $J$, $\Omega$, and the torsion classes. By extending the universal ansatz to include the $W_3$ torsion component and specializing to $W_2=0$, the authors derive algebraic conditions for fluxes that yield four-dimensional de Sitter vacua and identify a concrete example on SU(2)×SU(2) (the ten-dimensional lift of a known solution). They analyze group-manifold realizations, establish de Sitter no-go constraints for several algebras, and show that only SU(2)×SU(2) can satisfy all requirements within their ansatz, with the solution exhibiting tachyonic instabilities. The work highlights the potential abundance of universal dS solutions and the challenges of achieving metastability, while also outlining avenues to broaden the search beyond homogeneous geometries and consider backreaction and IIB analogues. Overall, it provides a geometrical, ten-dimensional framework for identifying and analyzing universal de Sitter vacua at tree level.

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.

Figures (3)

• Figure 1: $\Lambda/(f_1)^2$ as a function of $f_2/f_1$, for $c_3=8/\sqrt{3}$ and $f_3=f_4=0$. The area close to the horizontal axis is shown in more detail such that the dS solutions (in green) are visible. AdS solutions are shown in red and Minkowski solutions in blue.
• Figure 2: $w_3/W_1$ as a function of $f_2/f_1$, for $c_3=8/\sqrt{3}$. dS solutions are green, AdS solutions red and Minkowski solutions blue.
• Figure 3: Negative eigenvalues of the mass matrix $M^2/(f_1)^2$ for our line of dS solutions.