  We consider a self-interacting scalar field whose mass saturates the
Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a
negative cosmological constant in D \geq 3 dimensions. It is shown that the
asymptotic behavior of the metric has a slower fall-off than that of pure
gravity with a localized distribution of matter, due to the back-reaction of
the scalar field, which has a logarithmic branch decreasing as r^{-(D-1)/2} ln
r for large radius r.
  We find the asymptotic conditions on the fields which are invariant under the
same symmetry group as pure gravity with negative cosmological constant
(conformal group in D-1 dimensions). The generators of the asymptotic
symmetries are finite even when the logarithmic branch is considered but
acquire, however, a contribution from the scalar field.
