New constraints on classical de Sitter: flirting with the swampland

TL;DR

This work develops a 4d scalar potential V(ρ,τ,σ) for type II supergravities with parallel D_p/O_p sources to analyze classical de Sitter solutions. By deriving the full potential from 10d and showing the equivalence between 4d extrema and 10d equations of motion, the authors test stability via the three-scalar system and apply it to group-manifold compactifications with constant fluxes. They obtain strong no-go results ruling out de Sitter solutions on many nilmanifolds, semi-simple manifolds, and some solvmanifolds, while uncovering a small stability island in which all three scalars could be stabilized for certain λ-parametrized regions (0<λ<1/17 for p=6; 0<λ<1/10 for p=4,5). The findings contribute to swampland discussions by highlighting how higher-dimensional consistency conditions, such as the Bianchi identities, constrain 4d de Sitter realizations and guiding future exploration of intersecting-source configurations.

Abstract

We study the existence and stability of classical de Sitter solutions of type II supergravities with parallel Dp-branes and orientifold Op-planes. Together with the dilaton and volume scalar fields, we consider a third one that distinguishes between parallel and transverse directions to the Dp/Op. We derive the complete scalar potential for these three fields. This formalism allows us to reproduce known constraints obtained in 10d, and to derive new ones. Specifying to group manifolds with constant fluxes, we exclude a large region of parameter space, forbidding de Sitter solutions on nilmanifolds, semi-simple group manifolds, and some solvmanifolds. In the small remaining region, we identify a stability island, where the three scalars could be stabilized in any de Sitter solution. We discuss these results in the swampland context.