String versus Einstein frame in an AdS/CFT induced quantum dilatonic brane-world universe

An AdS/CFT induced quantum dilatonic brane world where the 4D boundary is flat or a de Sitter (inflationary) or anti-de Sitter brane is considered. The classical brane tension is fixed but the boundary QFT produces the effective brane tension by means of the account of corresponding conformal anomaly induced effective action. This results in inducing brane worlds in accordance with the AdS/CFT setup as warped compactification. The explicit. independent construction of quantum induced dilatonic brane worlds in two frames, the string and Einstein frames, is done. Their complete equivalency is demonstrated for all quantum cosmological brane worlds under discussion. including several examples of classical brane-world black holes. This is different from quantum corrected 4D dilatonic gravity where a de Sitter solution exists in the Einstein but not in the Jordan (string) frame. The role of quantum corrections in massive graviton perturbations around an anti-de Sitter brane is briefly discussed.