Stability Constraints on Classical de Sitter Vacua

TL;DR

The paper tackles the problem of realizing stable classical de Sitter vacua in Type II string theory by deriving no-go theorems for de Sitter extrema using a 4D potential built from curvature, fluxes, and orientifold planes. It introduces a no-go operator D = - a τ ∂_τ - b ρ ∂_ρ and shows that, under certain positivity conditions, positive-energy extrema cannot exist, highlighting the need for additional ingredients to evade the bound. A detailed stability analysis, via Sylvester's criterion on the universal moduli subspace, reveals that minimal evasion setups typically harbor tachyons or flat directions, ruling out metastable de Sitter vacua in those cases. By incorporating more fluxes and/or orientifolds, some configurations can evade both extremum and stability no-goes, outlining minimal ingredient sets that may allow (meta)stable classical de Sitter vacua, subject to nontrivial parameter constraints and approximations such as smeared sources and potential warping. The results illuminate the delicate balance required to achieve classical de Sitter solutions without non-perturbative effects or SUSY-breaking localized sources, and they map out a landscape where stable vacua demand richer internal structures.

Abstract

We present further no-go theorems for classical de Sitter vacua in Type II string theory, i.e., de Sitter constructions that do not invoke non-perturbative effects or explicit supersymmetry breaking localized sources. By analyzing the stability of the 4D potential arising from compactification on manfiolds with curvature, fluxes, and orientifold planes, we found that additional ingredients, beyond the minimal ones presented so far, are necessary to avoid the presence of unstable modes. We enumerate the minimal setups for (meta)stable de Sitter vacua to arise in this context.