Non-locally regularized antibracket-antifield formalism and anomalies in chiral W3 gravity

Abstract

The non-local regularization method, recently proposed by Evans et al., and Kleppe and Woodward, is extended to general gauge theories by reformulating it along the ideas of the antibracket-antifield formalism. From the interplay of both frameworks a fully regularized version of the field-antifield (FA) formalism arises, being able to deal with higher order loop corrections and to describe higher order loop contributions to the BRST anomaly. The quantum master equation, considered in the FA framework as the quantity parametrizing BRST anomalies, is argued to be incomplete at two and higher order loops and conjectured to reproduce only the one-loop corrections to the h ̵ p anomaly generated by the addition of O( h ̵ k) , k < p, counterterms. Chiral W 3 gravity is used to exemplify the non-locally regularized FA formalism. First, the regularized one-loop quantum master equation is used to compute the complete one-loop anomaly. Its two-loop order, however, is shown to reproduce only the modification to the two-loop anomaly produced by the addition of a suitable one-loop counterterm, thereby providing an explicit verification of the previous statement for p = 2. The well-known universal two-loop anomaly, instead, is alternatively obtained from the BRST variation of the non-locally regulated effective action. Incompleteness of the quantum master equation is thus concluded to be a consequence of a naive derivation of the FA BRST Ward identity.