The Effective Action of W3 Gravity to All Orders
Jan de Boer, Jacob Goeree
Abstract
The effective action for chiral W3 gravity is studied. It is shown that the computation of the effective action can be reduced to that of a SL(3,) 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 multiplicative renormalization constants of the WZW model are discussed and it is analyzed which particular values of these constants are consistent with previous one-loop calculations, and which reproduce the KPZ formulas for gravity and their generalizations for W3 gravity.
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