KPZ Analysis for W3 Gravity
Jan de Boer, Jacob Goeree
Abstract
Starting from the covariant action for W3 gravity, we discuss the BRST quantization of W3 gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld--Sokolov reduction for Sl(3,). Nilpotency of this charge leads to the KPZ formula for W3. In the conformal gauge, where the covariant action reduces to a Toda action, the BRST charge is equivalent to the one recently constructed by Bershadsky et al.
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