  We consider a 3-brane of positive cosmological constant (de Sitter) in
D-dimensional Minkowski space. We show that the Poincare algebra in the bulk
yields a SO(4,2) algebra when restricted to the brane. In the limit of zero
cosmological constant (flat brane), this algebra turns into the conformal
algebra on the brane. We derive a correspondence principle for Minkowski space
analogous to the AdS/CFT correspondence. We discuss explicitly the cases of
scalar and gravitational fields. For a 3-brane of finite thickness in the
transverse directions, we obtain a spectrum for vector gravitational
perturbations which correspond to vector mesons. The spectrum agrees with the
one obtained in truncated AdS space by de Teramond and Brodsky provided D=10
and the bulk mass scale M is of order the geometric mean of the Planck mass
($\bar M$) on the brane and $\Lambda_{QCD}$ ($M \sim (\bar M
\Lambda_{QCD})^{1/2} \sim 10^9$ GeV).
