W Gravity From Chern--Simons Theory
Jan de Boer, Jacob Goeree
Abstract
Starting with three dimensional Chern--Simons theory with gauge group $Sl(N,R)$, we derive an action $S_{cov}$ invariant under both left and right $W_N$ transformations. We give an interpretation of $S_{cov}$ in terms of anomalies, and discuss its relation with Toda theory.