Abstract
We review (mainly) quantum effects in the theories where the 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 the 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 the above effective action in the construction of nonsingular 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 nonzero temperature are calculated from d=5 dilatonic anti-de Sitter-like background solution which represents anti-de Sitter black hole for periodic time.
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