  We show that many of the recently proposed supersymmetric p-brane solutions
of d=10 and d=11 supergravity have the property that they interpolate between
Minkowski spacetime and a compactified spacetime, both being supersymmetric
supergravity vacua. Our results imply that the effective worldvolume action for
small fluctuations of the super p-brane is a supersingleton field theory for
$(adS)_{p+2}$, as has been often conjectured in the past.
