Canonical BRST Quantisation of Worldsheet Gravities

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.

27 pages. (Some factors of \hbar corrected)

References in corpus (6)

• Algebraic Structures and Differential Geometry in 2D String Theory
• Simplifications in Lagrangian BV quantization exemplified by the anomalies of chiral $W_3$ gravity
• Discrete States in the $W_3$ String
• $SL(\infty ,R)$ Symmetry of $W_{\infty }$ Gravity
• The Complete Cohomology of the W3 String
• The Multivalued Free-Field Maps of Liouville and Toda Gravities

Cited by in corpus (3)

• Antibracket, Antifields and Gauge-Theory Quantization
• The conformal gauge to the derivative gauge for worldsheet gravity
• Higher-loop anomalies in chiral gravities