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

TL;DR

This paper investigates the quantum stability and dynamical generation of dilatonic AdS backgrounds, exploring their holographic renormalization group flow and resulting boundary geometries influenced by quantum effects.

Contribution

It presents explicit examples of quantum-created dilatonic AdS spaces and analyzes the combined classical and quantum effective action in holographic RG context.

Findings

Quantum effects can induce the formation of dilatonic AdS spaces absent at classical level.

Explicit quantum creation of d4 dilatonic AdS Universe and d2 dilatonic AdS Black Hole demonstrated.

Quantum effects on the boundary can generate de Sitter or AdS geometries in the holographic framework.

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.