Does string theory have controlled metastable de Sitter vacua
In plain words
Our universe has a small positive vacuum energy. Whether string theory has a calculable solution of this kind that lives long enough is disputed.
Precise statement
Determine whether there exist solutions of string theory, with $\alpha'$ and $g_s$ corrections under control, whose 4D effective potential has a local minimum with $V > 0$ and lifetime longer than the Hubble time, such as KKLT or Large Volume Scenario constructions in type IIB orientifolds with anti-D3-brane uplift.
What would settle it
An explicit compactification with all corrections shown to be parametrically small, or a no-go theorem covering the controlled regimes.
Status in the literature
Unverified note
McAllister, Moritz, Nally and Schachner (2024) constructed explicit candidate KKLT de Sitter vacua at leading order in $\alpha'$ and $g_s$; control of higher corrections is disputed.