Absence of classical de Sitter with only parallel sources (Conjecture 1)

Prove that no classical de Sitter solutions of ten-dimensional type II supergravity compactifications exist when there is only a single set of parallel Dp/Op sources (i.e., only one brane/orientifold stack without intersections).

Background

Within the systematic classification of group-manifold compactifications used in the review, all known de Sitter solutions involve intersecting sources; the purely parallel case has resisted construction.

The authors summarize evidence and prior work suggesting a general no-go in this setup, but note that a complete proof remains outstanding.

References

"It is believed that \textsl{de Sitter solutions with only parallel sources, also referred to as one set of sources, do not exist} (Conjecture 1, )."

— Dark energy from string theory: an introductory review  (2603.25797 - Andriot, 26 Mar 2026) in Section 3.1.2, Existence of supergravity solutions (Conjecture 1)