Constraining de Sitter Space in String Theory

TL;DR

The paper tackles whether de Sitter space can emerge in string theory, focusing on the heterotic string and its high-curvature regime. It uses a world-sheet CFT framework with exact $SO(1,n)$ isometries realized by conserved currents, and a Wick-rotated, compact Euclidean theory with $SO(n+1)$ symmetry to derive stringent unitarity and central-charge constraints. The analysis shows that the left- and right-moving current algebras cannot consistently realize a $dS_n$ background for $n\ge 4$, ruling out classical de Sitter vacua in the heterotic string and casting doubt on similar landscape expectations. The work further interprets the findings in dual Type II orientifold contexts and discusses the limits of this no-go, including possible but not realized avenues for evasion and the distinct status of AdS cases.

Abstract

We argue that the heterotic string does not have classical vacua corresponding to de Sitter space-times of dimension four or higher. The same conclusion applies to type II vacua in the absence of RR fluxes. Our argument extends prior supergravity no-go results to regimes of high curvature. We discuss the interpretation of the heterotic result from the perspective of dual type II orientifold constructions. Our result suggests that the genericity arguments used in string landscape discussions should be viewed with caution.