  Given a Sasaki-Einstein manifold, M_7, there is the N=2 supersymmetric AdS_4
x M_7 Freund-Rubin solution of eleven-dimensional supergravity and the
corresponding non-supersymmetric solutions: the perturbatively stable
skew-whiffed solution, the perturbatively unstable Englert solution, and the
Pope-Warner solution, which is known to be perturbatively unstable when M_7 is
the seven-sphere or, more generally, a tri-Sasakian manifold. We show that
similar perturbative instability of the Pope-Warner solution will arise for any
Sasaki-Einstein manifold, M_7, admitting a basic, primitive, transverse
(1,1)-eigenform of the Hodge-de Rham Laplacian with the eigenvalue in the range
between 2(9-4\sqrt 3) and 2(9+4\sqrt 3). Existence of such (1,1)-forms on all
homogeneous Sasaki-Einstein manifolds can be shown explicitly using the Kahler
quotient construction or the standard harmonic expansion. The latter shows that
the instability arises from the coupling between the Pope-Warner background and
Kaluza-Klein scalar modes that at the supersymmetric point lie in a long
Z-vector supermultiplet. We also verify that the instability persists for the
orbifolds of homogeneous Sasaki-Einstein manifolds that have been discussed
recently.
