The induced action ofW 3 gravity

We obtain the induced action h, b] for chiralW ₃ gravity in thec± limit from the induced action of a gaugedSl(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 ofW ₃ gravity in which the currentsT andW become auxiliary fields. An explicit realization ofT andW in terms of the gauge fields is given. In terms of new fieldsr ands, which are a generalization of Polyakov'sf variable for ordinary gravity, the complete induced action h, b; c±] becomes local.Work supported in part by NSF grant No. PHYS 89-08495Address after September 1, 1991: Physics Department, U.C. Berkeley, Berkeley, CA 94720, USA