The Induced Action of I413 Gravity

We obtain the induced action F[h, b] for chiral W3 gravity in the c ~ ___ limit from the induced action of a gauged Sl(3, R) Wess-Zumino-Witten model by imposing constraints on the currents of the latter. In the process we find a closed gauge algebra for the gauge sector of W3 gravity in which the currents T and W become auxiliary fields. An explicit realization of T and W in terms of the gauge fields is given. In terms of new fields r and s, which are a generalization of Polyakov's f variable for ordinary gravity, the complete induced action l-'[h, b; c ~ _ 0o] becomes local.