New constraints on classical de Sitter: flirting with the swampland
  We study the existence and stability of classical de Sitter solutions of type
II supergravities with parallel Dp-branes and orientifold Op-planes. Together
with the dilaton and volume scalar fields, we consider a third one that
distinguishes between parallel and transverse directions to the Dp/Op. We
derive the complete scalar potential for these three fields. This formalism
allows us to reproduce known constraints obtained in 10d, and to derive new
ones. Specifying to group manifolds with constant fluxes, we exclude a large
region of parameter space, forbidding de Sitter solutions on nilmanifolds,
semi-simple group manifolds, and some solvmanifolds. In the small remaining
region, we identify a stability island, where the three scalars could be
stabilized in any de Sitter solution. We discuss these results in the swampland
context.
