Higher-loop anomalies in chiral gravities

Abstract

The one-loop anomalies for chiral $W_3$ gravity are derived using the Fujikawa regularisation method. The expected two-loop anomalies are then obtained by imposing the Wess-Zumino consistency conditions on the one-loop results. The anomalies found in this way agree with those already known from explicit Feynman diagram calculations. We then directly verify that the order ${\hslash }^2$ non-local BRST Ward identity anomalies, arising from the ``dressing'' of the one-loop results, satisfy Lam's theorem. It is also shown that in a rigorous calculation of $Q^2$ anomaly for the BRST charge, one recovers both the non-local as well as the local anomalies. We further verify that, in chiral gravities, the non-local anomalies in the BRST Ward identity can be obtained by the application of the anomalous operator $Q^2$, calculated using operator products, to an appropriately defined gauge fermion. Finally, we give arguments to show why this relation should hold generally in reparametrisation-invariant theories.

21 pages, latex, 12 figures as uuencoded postscript. To appear in Nucl. Phys. B

References in corpus (3)

• Simplifications in Lagrangian BV quantization exemplified by the anomalies of chiral $W_3$ gravity
• Canonical BRST Quantisation of Worldsheet Gravities
• Path-integral quantization of $W_{\infty }$ gravity

Cited by in corpus (2)

• Higher Loop Anomalies and their Consistency Conditions in Nonlocal Regularization
• The BPHZ renormalised BV master equation and Two-loop Anomalies in Chiral Gravities