CONDITIONS FOR ANOMALY-FREE-W AND SUPER-W ALGEBRAS
Additional Document Info
We construct the BRST charge for the W, W1+ and super-W algebras. The criterion of nilpotency in general gives divergent expressions for the central charge, which can be regularised using zeta-function techniques. We discuss the ambiguities inherent in such procedures, and present a well-defined prescription for regularising all the higher-spin anomalies. Since the ghost system should provide a realisation of the algebra, the anomaly-cancellation conditions must be consistent for all spin levels, provided that the regularisation scheme is a consistent one, and we verify this explicitly up to spin 18. For W, we find c=-2, in agreement with a recent investigation where the spin 2, 3 and 4 anomalies were examined. For W1+, we find that anomaly-freedom requires c=0, whilst for super-W, we find c=-2, implying that the total central charge is 3 2c=-3. We find that the intercept 0 is zero for all the algebras W, W1+ and super W. 1991.