The de Sitter swampland conjecture and supersymmetric AdS vacua

TL;DR

The paper analyzes the claim that string theory forbids de Sitter critical points under the swampland criterion $|\nabla V| \ge c\,V$, arguing that in several well-studied moduli-stabilisation scenarios this constraint is even stronger because it also forbids supersymmetric AdS vacua. Focusing on a 1-modulus no-scale regime in Type IIB flux compactifications, the authors show that large-volume behavior, dominated by the $\mathcal{R}^4$ $(\alpha')^3$ correction, drives $V$ toward $0^+$ as $\mathrm{Re}(T) \to \infty$, so the existence of any SUSY vacuum with $W = W_0 + A e^{-a T}$ would necessitate a turnover and hence a de Sitter critical point. This leads to the conclusion that the conjecture, if true, would falsify known supersymmetric AdS solutions in these models, making the claim extraordinarily strong. The analysis also notes that, while de Sitter critical points do not automatically yield de Sitter vacua, the argument applies to many prominent compactifications and has implications for both Type IIB and heterotic dilaton stabilization.

Abstract

It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.