QUANTUM EQUIVALENCE AND THE RENORMALIZATION-GROUP IN THE MODELS OF 2-DIMENSIONAL DILATON GRAVITY

The family of (1 + 1)-dimensional models of dilation gravity described by the Lagrangian L = -square-rootg[1/2Z(PHI)g(munu)partial derivativ e(mu)PHIpartial derivative(nu)PHI + C(PHI)R + V(PHI)] with an arbitrar y set T(PHI) = {Z(PHI); C(PHI); V(PHI)} of functions of the dilation f ield is considered. The dependence of the one-loop structure of renorm alizations on the choice of T(PHI) is studied. Generalization to the c ase of Maxwell-dilaton gravity is discussed. A renormalization group ( RG) is constructed for the generalized coupling constants T(PHI), and RG fixed points are found. It is proved that the Callan-Giddings-Harve y-Strominger model is not a one-loop fixed point. The problem of quant um equivalence of classically equivalent models with different T(PHI) is studied by considering a specific example. It is shown that, in the one-loop approximation, equivalence is maintained only on the mass sh ell and that, on-shell divergences of the effective action are surface terms. As an application, one-loop divergences of (1 + 1)-dimensional R2-gravity are calculated using a simple method.