Quantum (in)stability of dilatonic AdS backgrounds and the holographic renormalization group with gravity

The stability of dilatonic AdS spaces due to quantum effects of dilaton coupled conformal matter is considered. When such spaces do not exist on a classical level, their dynamical generation occurs. Explicit examples corresponding to the quantum creation of a 4D dilatonic AdS universe and a 2D dilatonic AdS black hole (BH) are presented. Motivated by the holographic RG, in a similar approach, the complete 5D effective action is discussed. The intermediate region where it is the sum of two parts, the bulk (classical gravity) and boundary quantum action, is investigated. The effective equation solution representing a 5D AdS universe with a warp scale factor is found. A four-dimensional de Sitter or AdS world is generated on the boundary of such a universe as a result of quantum effects.