ONE-LOOP RENORMALIZATION OF THE 4-DIMENSIONAL THEORY FOR QUANTUM DILATON GRAVITY

We study one-loop renormalization in the most general metric-dilaton t heory with second derivative terms only, The classical action includes three arbitrary functions of the dilaton. The general theory can be d ivided into two classes: models of one are equivalent to gravity confo rmally coupled to a scalar held and also to general relativity with a cosmological term, The models of the second class have one extra degre e of freedom which corresponds to the dilaton. We calculate the one-lo op divergences for the models of the second class and find that the th eory is not renormalizable off the mass shell. At the same time the ar bitrary functions of the dilaton in the starting action can be fine-tu ned in such a way that an the higher derivative counterterms disappear on shell. The only structures in both the classical action and counte rterms, which survive on shell, are the potential (cosmological) ones. They can be removed by renormalization of the dilaton field that acqu ires the nontrivial anomalous dimension, which leads to the effective running of the cosmological constant. Another application of our calcu lations is the following. For some special choice of the arbitrary fun ctions our dilaton model is equivalent to general relativity with an a dditional R(2) term. Such an equivalence holds at the quantum level if we do not introduce the external source for the dilaton field. Thus o ur calculations in a general dilaton model in original variables inclu de quantum Lambda + alpha R + beta R(2) theory as the particular case.