Correspondence principle for a brane in Minkowski space and vector mesons

We consider a 3-brane of positive cosmological constant (de Sitter) inD-dimensional Minkowski space. We show that the Poincare algebra in the bulkyields a SO(4,2) algebra when restricted to the brane. In the limit of zerocosmological constant (flat brane), this algebra turns into the conformalalgebra on the brane. We derive a correspondence principle for Minkowski spaceanalogous to the AdS/CFT correspondence. We discuss explicitly the cases ofscalar and gravitational fields. For a 3-brane of finite thickness in thetransverse directions, we obtain a spectrum for vector gravitationalperturbations which correspond to vector mesons. The spectrum agrees with theone obtained in truncated AdS space by de Teramond and Brodsky provided D=10and 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).Comment: 8 pages in two-column ReVTeX