Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-05-16
Nucl.Phys. B454 (1995) 207-226
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, latex, 12 figures as uuencoded postscript. To appear in Nucl. Phys. B
Scientific paper
10.1016/0550-3213(95)00401-D
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 $\hbar^2$ 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.
Mohayaee Roya
Wenham L.
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