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

TL;DR

This work investigates quantum stability and dynamical generation of dilatonic AdS backgrounds by incorporating anomaly-induced effective actions of conformal matter. Using dilaton-coupled fermions, the authors derive quantum-corrected equations that admit a quantum-created dilatonic AdS universe in 4d and a quantum-induced 2d dilatonic AdS black hole, even when these configurations are absent classically. They extend the analysis to a holographic RG framework, coupling a 5d AdS bulk to a boundary quantum action, and show that quantum boundary effects can induce a warped geometry with a de Sitter boundary or, in RS-like setups, a 4d AdS wall with dynamical boundary gravity. The results reveal a mechanism for quantum-induced AdS regions and provide a groundwork for gravity on the boundary to emerge from quantum effects in AdS/CFT contexts.

Abstract

Stability of dilatonic AdS spaces due to quantum effects of dilaton coupled conformal matter is considered. When such spaces do not exist on classical level, their dynamical generation occurs. Explicit examples corresponding to quantum creation of d4 dilatonic AdS Universe and of d2 dilatonic AdS Black Hole (BH) are presented. Motivated by holographic RG, in the similar approach the complete d5 effective action is discussed. The intermediate region where it is the sum of two parts: bulk (classical gravity) and boundary quantum action is investigated. The effective equations solution representing d5 AdS Universe with warp scale factor is found. Four-dimensional de Sitter or AdS world is generated on the boundary of such Universe as a result of quantum effects.