Quantum dilatonic gravity in d = 2,4 and 5 dimensions

TL;DR

This paper reviews quantum effects in dilatonic gravity across 2, 4, and 5 dimensions, focusing on effective actions, black hole thermodynamics, cosmology, and AdS/CFT correspondence.

Contribution

It provides new calculations of effective actions, quantum corrections, and applications to black holes, cosmology, and gauge/gravity duality in various dimensions.

Findings

One-loop effective actions for 2d and 4d dilatonic gravity are evaluated.

Quantum corrections to black hole parameters are computed.

Boundary gauge theory potentials are derived from 5d dilatonic backgrounds.

Abstract

We review (mainly) quantum effects in the theories where gravity sector is described by metric and dilaton. The one-loop effective action for dilatonic gravity in two and four dimensions is evaluated. Renormalization group equations are constructed. The conformal anomaly and induced effective action for 2d and 4d dilaton coupled theories are found. It is applied to study of quantum aspects of black hole thermodynamics, like calculation of Hawking radiation and quantum corrections to black hole parameters and investigation of quantum instability for such objects with multiple horizons. The use of above effective action in the construction of non-singular cosmological models in Einstein or Brans-Dicke (super)gravity and investigation of induced wormholes in supersymmetric Yang-Mills theory are given. 5d dilatonic gravity (bosonic sector of compactified IIB supergravity) is discussed in connection with bulk/boundary (or AdS/CFT) correspondence. Running gauge coupling and quark-antiquark potential for boundary gauge theory at zero or non-zero temperature are calculated from d=5 dilatonic Anti-de Sitter-like background solution which represents Anti-de Sitter black hole for periodic time.