String tension between de Sitter vacua and curvature corrections
Ivano Basile, Alessia Platania
Abstract
Higher-derivative corrections to cosmological effective actions in string theory are largely constrained by T-duality, but have been computed hitherto only to the first few orders in the string scale ${\ensuremath{\alpha}}^{\ensuremath{'}}$. The functional renormalization group, in conjunction with the strong constraints imposed by T-duality, allows us to derive cosmological effective actions to all orders in ${\ensuremath{\alpha}}^{\ensuremath{'}}$ while avoiding ``truncations'' of the theory space. We show that the resulting higher-derivative ${\ensuremath{\alpha}}^{\ensuremath{'}}$-corrections forbid the existence of de Sitter vacua, at least in regimes where string-loop corrections can be neglected. Our findings thus support the no-de Sitter swampland conjecture in the presence of all-order effects in ${\ensuremath{\alpha}}^{\ensuremath{'}}$.