A note on obstinate tachyons in classical dS solutions

The stabilisation of the dilaton and volume in tree-level flux compactifications leads to model independent and thus very powerful existence and stability criteria 14 dS solutions. In this paper we show that the sizes of cycles wrapped by orientifold planes are scalars whose scalings in the potential are not entirely model independent, but enough to entail strong stability constraints. For all known dS solutions arising from massive IIA supergravity flux compactifications on SU(3)-structure manifolds the tachyons are exactly within the subspace spanned by the dilaton, the total volume and the volumes of the orientifold cycles. We illustrate this in detail for the well-studied case of the O6 plane compactification on SU(2) x SU(2)/Z(2) x Z(2). For that example we uncover another novel structure in the tachyon spectrum: the dS solutions have a singular, but supersymmetric, Minkowski limit, in which the tachyon exactly aligns with the sgoldstino.