AdS/CFT correspondence, conformal anomaly and quantum corrected entropy bounds

The role of conformal anomaly in AdS/CFT and related issues is clarified. The comparison of holographic and QFT conformal anomalies (with the account of brane quantum gravity contribution) indicates the possibility for brane quantum gravity to occur within the AdS/CFT setup. Three-dimensional quantum induced inflationary (or hyperbolic) brave-world is shown to be realized in the frames of AdS3/CFT2 correspondence where the role of 2d brane cosmological constant is played by effective tension due to two-dimensional conformal anomaly. The dynamical equations to describe 4d FRW universe with the account of quantum effects produced by conformal anomaly are obtained. The quantum corrected energy, pressure and entropy are found. The dynamical evolution of entropy bounds in the inflationary universe is estimated and its comparison with quantum corrected entropy is done. It is demonstrated that entropy bounds for quantum corrected entropy are getting the approximate ones and occur for some limited periods of evolution of the inflationary universe.