We show that many of the recently proposed supersymmetric p-brane solu
tions of d = 10 and d = 11 supergravity have the property that they in
terpolate between Minkowski spacetime and a compactified spacetime, bo
th being supersymmetric supergravity vacua. Our results imply that the
effective world-volume action for small fluctuations of the super p-b
rane is a supersingleton field theory for (p+2)-dimensional anti-de Si
tter spacetime, as has been often conjectured in the past.