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Prove classical stability of the constructed de Sitter solutions

Provide a rigorous proof of the classical stability of the four-dimensional de Sitter solutions obtained from six-dimensional gauged chiral supergravity derived from F-theory, for example by establishing the absence of growing perturbation modes and tachyonic instabilities.

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Background

Beyond existence, the physical relevance of de Sitter solutions hinges on their stability. The authors indicate that demonstrating stability rigorously remains unresolved.

A full perturbative (and possibly non-perturbative) stability analysis would be decisive for assessing the viability of the constructed vacua.

References

Although the existence classical de Sitter solutions to the equations we solve is incontrovertible, several points remain open. These include the description of the full F-theory solutions with all moduli stabilized for concrete models, a better understanding of the singularities, a rigorous proof of the stability of the solutions and so on.

— 4D de Sitter from String Theory via 6D Supergravity (2408.03852 - Burgess et al., 7 Aug 2024) in Section: Conclusions