Canonical BRST Quantisation of Worldsheet Gravities

TL;DR

This paper presents a simplified BRST quantisation method for worldsheet gravities, employing a derivative gauge and momenta introduction, leading to clearer anomaly evaluation and canonical transformation properties.

Contribution

It introduces a novel reformulation of BRST quantisation for worldsheet gravities using a derivative gauge and momenta, simplifying anomaly calculations and canonical transformations.

Findings

Simplified BRST formulation for Virasoro and W3 gravities.

New expression for anomalies via the anomalous operator Q^2.

Transformation rules form a canonical transformation generated by Q.

Abstract

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.