THE EFFECTIVE ACTION OF W(3) GRAVITY TO ALL ORDERS

The effective action for chiral W3 gravity is studied. It is shown tha t the computation of the effective action can be reduced to that of a SL(3, R) Wess-Zumino-Witten theory. If one assumes that the effective action for the Wess-Zumino-Witten model is identical to the WZW action up to multiplicative renormalizations, then the effective action for W3 gravity is, to all orders, given by a constrained WZW model. The mu ltiplicative renormalization constants of the WZW model are discussed and it is analyzed which particular values of these constants are cons istent with previous one-loop calculations, and which reproduce the KP Z formulas for gravity and their generalizations for W3 gravity.