On classical de Sitter solutions in higher dimensions

TL;DR

This work derives necessary criteria for classical meta-stable de Sitter solutions in higher-dimensional flux compactifications of type II supergravity, showing that viable models are severely restricted as dimensions grow. By exploiting the universal dependence of the tree-level potential on the volume modulus ρ and the dilaton-related scale τ, the author identifies that meta-stable de Sitter vacua can occur only in a few cases: O6 compactifications to D=5,6 and O5 compactifications to D=5, all requiring negatively curved internal spaces. No meta-stable de Sitter solutions exist for D>6, and the surviving D=5,6 scenarios have a common feature of negative internal curvature and negative net orientifold tension. The results sharpen the understanding of de Sitter model-building in string theory and highlight the crucial roles of curvature and source tension, while noting the limitations of smeared-source approximations and suggesting avenues for broader exploration and duality checks.

Abstract

We derive necessary criteria for the existence of classical, meta-stable, de Sitter solutions in flux compactifications of type II supergravity down to dimensions higher than four. We find that the possibilities in higher dimensions are much more restricted than in four dimensions. The only models that satisfy the criteria are derived from O6 compactifications to D=5,6 and O5 compactifications to D=5 and no meta-stable solutions can exist in dimensions higher than six. All these models have in common that the compact dimensions are negatively curved.