TRACE-ANOMALY-INDUCED EFFECTIVE ACTION FOR 2D AND 4D DILATON COUPLED SCALARS

The spherically symmetric reduction of higher-dimensional Einstein-sca lar theory leads to a lower-dimensional dilatonic gravity with a dilat on coupled scalar [for example, from a four-dimensional (4D) to a 2D s ystem]. We calculate the trace anomaly and anomaly-induced effective a ction for 2D and 4D dilaton coupled scalars. The large-N effective act ion for 2D quantum dilaton-scalar gravity is also found. These 2D resu lts may be applied to the analysis of 4D spherical collapse. The role of new, dilaton-dependent terms in the trace anomaly for 2D black hole s and Hawking radiation is investigated in some specific models of dil atonic gravity which represent a modification of the Callan-Giddings-H arvey-Strominger model. The conformal sector for 4D dilatonic gravity is constructed. The quantum back reaction of dilaton coupled matter is briefly discussed (it may lead to an inflationary universe with a non trivial dilaton).