HIGHER-LOOP ANOMALIES IN CHIRAL GRAVITIES

The one-loop anomalies for chiral W-3 gravity are derived using the Fu jikawa regularisation method. The expected two-loop anomalies are then obtained by imposing the Wess-Zumino consistency conditions on the on e-loop results. The anomalies found in this way agree with those alrea dy known from explicit Feynman diagram calculations We then directly v erify that the order H BAR(2) non-local BRST Ward identity anomalies, arising from the ''dressing'' of the one-loop results, satisfy Lam's t heorem. It is also shown that in a rigorous calculation of Q(2) anomal y 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 appli cation of the anomalous operator Q(2), calculated using operator produ cts, to an appropriately defined gauge fermion. Finally, we give argum ents to show why this relation should hold generally in reparametrisat ion-invariant theories.