The Effective Action of $W_3$ Gravity to All Orders

Abstract

The effective action for chiral $W_3$ gravity is studied. It is shown that the computation of the effective action can be reduced to that of a $SL(3,\re)$ Wess-Zumino-Witten theory. If one assumes that the effective action for the Wess-Zumino-Witten model is identical to the WZW action up to multiplicative renormalizations, then the effective action for $W_3$ gravity is, to all orders, given by a constrained WZW model. The multiplicative renormalization constants of the WZW model are discussed and it is analyzed which particular values of these constants are consistent with previous one-loop calculations, and which reproduce the KPZ formulas for gravity and their generalizations for $W_3$ gravity.

22 pages, THU-92/33

References in corpus (4)

• Lectures on W algebras and W gravity
• W Gravity From Chern--Simons Theory
• The Covariant W_3 Action
• Classical and Quantum W-Gravity

Cited by in corpus (9)

• Antibracket, Antifields and Gauge-Theory Quantization
• Conformal sigma models corresponding to gauged Wess-Zumino-Witten theories
• Non-linear finite $W$-symmetries and applications in elementary systems
• Representation theory of finite W algebras
• KPZ Analysis for $W_3$ Gravity
• On the Lagrangian Realization of Non-Critical $\mathcal{W}$-Strings
• Regularisation of non-local actions in two-dimensional field theories
• Ward Identities and Anomalies in Pure W_4 Gravity
• Effective Action and Exact Geometry in Chiral Gauged WZW Models