Systematic instability of classical de Sitter solutions (Conjecture 2)

Show that any classical de Sitter solution arising as a string background in the regimes considered (e.g., type II supergravity compactifications) possesses at least one perturbative tachyonic direction, i.e., is necessarily perturbatively unstable.

Background

The conjecture, originating in prior work summarized here, is supported by all currently known explicit ten-dimensional supergravity de Sitter solutions on group manifolds, which exhibit tachyonic directions with η_V \lesssim −1.

A general proof remains elusive, and the authors review partial results and methods that have so far fallen short of a complete theorem.

References

"Summarizing the status, it has been proposed in (conjecture 2) that \textsl{all solutions with a de Sitter spacetime, obtained as a string background in a classical regime, are perturbatively unstable}."

— Dark energy from string theory: an introductory review  (2603.25797 - Andriot, 26 Mar 2026) in Section 2.2.3, Stability no-go theorems

At present, we do not have the tools to study, in a simple manner, neither the perturbative stability of the generic de Sitter solutions, nor that of the specific S-fold we considered.

— de Sitter and S-folds in type IIB from $\mathcal{N} = 4$ $D = 4$ gauged supergravity  (2609.05004 - Sterckx, 4 Sep 2026) in Section 6, subsection "Outlook", paragraph "Perturbative stability"