Abstract
The stability of anti-deSitter background solutions of gravity/scalar systems with respect to small fluetuations of the scalar fields is analyzed. As in the four dimensional case, one finds stability even about a local maximum provided that the effective scalar field masses are not “too tachyonic,” and for sufficiently low mass there are two possible boundary conditions that allow a well-defined and conserved energy. Unlike the
d = 4 case only one boundary condition is applicable to the known gauged supergravity theories in
d = 5 and
d = 7. For
d = 7 the stability criterion is satisfied while for
d = 5 stability is marginal.
