KPZ Analysis for $W_3$ Gravity

Abstract

Starting from the covariant action for $W_3$ gravity, we discuss the BRST quantization of $W_3$ gravity. Taking the chiral gauge the BRST charge has a natural interpretation in terms of the quantum Drinfeld--Sokolov reduction for $Sl(3,\re)$. Nilpotency of this charge leads to the KPZ formula for $W_3$. 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.

26 pages, THU-92/34

References in corpus (8)

• W-symmetry in Conformal Field Theory
• Covariant $W$ Gravity \& its Moduli Space from Gauge Theory
• Lectures on W algebras and W gravity
• W Gravity From Chern--Simons Theory
• A Derivation of the BRST Operator for Non-Critical W-Strings
• The Covariant W_3 Action
• Classical and Quantum W-Gravity
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Cited by in corpus (5)

• On the Landau-Ginzburg Realization of Topological Gravities
• Generalized Drinfeld-Sokolov Hierarchies, Quantum Rings, and W-Gravity
• On the Algebraic Structure of Gravitational Descendants in CP(n-1) Coset Models
• On the Cohomology of the Noncritical $W$-string
• The W_3 algebra: modules, semi-infinite cohomology and BV-algebras