PERTURBATIVE FINITENESS OF INDUCED 2-DIMENSIONAL QUANTUM-GRAVITY

A detailed investigation of a local version of two-dimensional induce quantum gravity is presented. The renormalization procedure includes a conformal transformation of the metric. The one-loop divergences are calculated for a nonminimal gauge of sufficiently general form. It is established that the counterterms are gauge-dependent. For one of the conformally equivalent versions of the theory all the counterterms vanish for a certain value of a gauge parameter. All the beta-functions are equal to zero, independently of the values of the gauge parameters.