We point out that massive gauged supergravity potentials, for example those
arising due to the massive breathing mode of sphere reductions in M-theory or
string theory, allow for supersymmetric (static) domain wall solutions which
are a hybrid of a Randall-Sundrum domain wall on one side, and a dilatonic
domain wall with a run-away dilaton on the other side. On the anti-de Sitter
(AdS) side, these walls have a repulsive gravity with an asymptotic region
corresponding to the Cauchy horizon, while on the other side the runaway
dilaton approaches the weak coupling regime and a non-singular attractive
gravity, with the asymptotic region corresponding to the boundary of spacetime.
We contrast these results with the situation for gauged supergravity potentials
for massless scalar modes, whose supersymmetric AdS extrema are generically
maxima, and there the asymptotic regime transverse to the wall corresponds to
the boundary of the AdS spacetime. We also comment on the possibility that the
massive breathing mode may, in the case of fundamental domain-wall sources,
stabilize such walls via a Goldberger-Wise mechanism.Comment: latex file, 11 pages, 3 figure