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

AdS/CFT induced quantum dilatonic brane-world where 4d boundary is flat or de Sitter (inflationary) or Anti-de Sitter brane is considered. The classical brane tension is fixed but boundary QFT produces the effective brane tension via the account of corresponding conformal anomaly induced effective action. This results in inducing of brane-worlds in accordance with AdS/CFT set-up as warped compactification. The explicit, independent construction of quantum induced dilatonic brane-worlds in two frames: string and Einstein one is done. It is demonstrated their complete equivalency 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 de Sitter solution exists in Einstein but not in Jordan (string) frame. The role of quantum corrections on massive graviton perturbations around Anti-de Sitter brane is briefly discussed.