THE BPHZ RENORMALIZED BV MASTER EQUATION AND 2-LOOP ANOMALIES IN CHIRAL GRAVITIES

Anomalies and BRST invariance are governed, in the context of Lagrangi an Batalin-Vilkovisky quantisation, by the master equation, whose clas sical limit is (S,S) = 0. Using Zimmerman's normal products and the BP HZ renormalisation method, we obtain a corresponding local quantum ope rator equation, which is valid to all orders in perturbation theory. T he formulation implies a calculational method for anomalies that is us eful also outside this context and that remains completely within regu larised perturbation theory. It makes no difference in principle wheth er the anomaly appears at one loop or at higher loops, The method is i llustrated by computing the one and two-loop anomalies in chiral W-3 g ravity.