On (A)dS Solutions from Scherk-Schwarz Orbifolds

TL;DR

This paper explores the possibility of de Sitter vacua in string theory compactifications, deriving no-go theorems, presenting explicit solutions, and analyzing their stability and control within effective field theories.

Contribution

It provides new no-go theorems for dS solutions, explicitly constructs a dS and an AdS solution, and analyzes their stability and parametric control in string compactifications.

Findings

No fully controlled dS solutions found; existing solutions have instabilities.

Explicit dS and AdS solutions constructed, with the AdS being controllable.

Universal tachyon present in dS solutions, indicating instability.

Abstract

We investigate the existence of dS vacua in supersymmetry-breaking Scherk-Schwarz toroidal compactifications of type II string theory, using the well-understood ingredients of curvature, fluxes and 1-loop Casimir energy. Starting from the 10d equations, we derive a series of no-go theorems and existence conditions for dS, and present two explicit, fully-backreacted, solutions: a dS one, which turns out to be not under control, and an AdS one, which can be chosen at arbitrarily weak coupling and large volume by dialling the unbounded fluxes. We then use a lower-dimensional EFT description to show that any dS solution has a universal tachyon and no parametric control. The simplest AdS solutions are also perturbatively unstable. We extend the no-go theorems to slow-roll acceleration and test various swampland conjectures in our non-supersymmetric string setup. The question of numerically controlled, unstable dS is left open.