Systematic instability of classical de Sitter solutions (Conjecture 2)

Show that any classical de Sitter solution arising as a string background in the regimes considered (e.g., type II supergravity compactifications) possesses at least one perturbative tachyonic direction, i.e., is necessarily perturbatively unstable.

Background

The conjecture, originating in prior work summarized here, is supported by all currently known explicit ten-dimensional supergravity de Sitter solutions on group manifolds, which exhibit tachyonic directions with η_V \lesssim −1.

A general proof remains elusive, and the authors review partial results and methods that have so far fallen short of a complete theorem.