KPZ ANALYSIS FOR W3 GRAVITY

Starting from the covariant action for W3 gravity we constructed in a previous paper [Phys. Lett. B274 (1992) 289), we discuss the BRST quan tization of W3 gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld-Sokolov reduct ion for Sl(3, R). Nilpotency of this charge leads to the KPZ formula f or W3. In the conformal gauge, where the covariant action reduces to a Toda action, the BRST charge is equivalent to the one recently constr ucted by Bershadsky et al. [Phys. Lett. B292 (1992) 35].