Background gauge invariance in the antifield formalism for theories with open gauge algebras

We show that any BRST invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the antifield formalism, then the effective action possesses a local background gauge invariance. The presence of antifields (BRST sources) is necessary. As an example we analyze chiral $W_3$ gravity.Comment: 17pp., Latex, mispelling in my name! corrected, no other change

Canonical BRST Quantisation of Worldsheet Gravities

We reformulate the BRST quantisation of chiral Virasoro and $W_3$ worldsheet gravities. Our approach follows directly the classic BRST formulation of Yang-Mills theory in employing a derivative gauge condition instead of the conventional conformal gauge condition, supplemented by an introduction of momenta in order to put the ghost action back into first-order form. The consequence of these simple changes is a considerable simplification of the BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino consistency conditions. In particular, the transformation rules of all fields now constitute a canonical transformation generated by the BRST operator $Q$, and we obtain in this reformulation a new result that the anomaly in the BRST Ward identity is obtained by application of the anomalous operator $Q^2$, calculated using operator products, to the gauge fermion.Comment: 27 pages. (Some factors of \hbar corrected

Path-integral quantization of W∞W_\infty gravity

We consider the anomalies of $W_\infty$ gravity in the context of path-integralquantization. We derive the ghost-loop anomalies to all orders in $\hbar$ directly from the path-integral measure by the Fujikawa method. We also show that in the matter sector the higher-loop anomalies can be obtained by implementation of the Wess-Zumino consistency condition using the one-loop anomaly. Cancellation of the anomalies between these two sectors then leaves the theory anomaly-free.Comment: 9 pages, Imperial/TP/93-94/43, Plain Te