THE RENORMALIZATION STRUCTURE AND QUANTUM EQUIVALENCE OF 2D DILATON GRAVITIES

The one-loop effective action corresponding to the general model of di laton gravity given by the Lagrangian L = - square-root g[1/2Z(PHI)g(m unu)partial derivative(mu)PHI partial derivative(nu)PHI + C(PHI)R + V( PHI)], where Z(PHI), C(PHI) and V(PHI) are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of cl assically equivalent dilaton gravities is studied. By specific calcula tion of explicit examples, it is shown that classically equivalent qua ntum gravities are also perturbatively equivalent at the quantum level , but only on-shell. The renormalization group equations for the gener alized effective couplings Z(PHI), C(PHI) and V(PHI) are written. An a nalysis of the equations shows, in particular, that the gravitational sector of the Callan-Giddings-Harvey-Strominger model is not a fixed p oint of these equations.