Absence of classical de Sitter with only two intersecting source sets (Conjecture 4)

Prove that classical de Sitter solutions of ten-dimensional type II supergravity compactifications cannot exist when there are only two intersecting sets of Dp/Op sources; show that at least three intersecting source sets are necessary.

Background

All known explicit supergravity de Sitter solutions presented in the review require at least three intersecting brane/orientifold sets.

The authors frame this empirical pattern as Conjecture 4 and discuss its implications, including the corollary that supersymmetric higher-dimensional theories (with more than four supercharges) should not admit such de Sitter solutions.