Nonlocally Regularized Antibracket-Antifield Formalism and Anomalies in Chiral $W_3$ Gravity

Abstract

The nonlocal regularization method, recently proposed in ref.\,\ct{emkw91,kw92,kw93}, 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 ${\hslash }^p$ anomaly generated by the addition of $O({\hslash }^k)$, $k<p$, counterterms. Chiral $W_3$ gravity is used to exemplify the nonlocally 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 nonlocally 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.

32 pages, LaTeX (uses feynman), 3 figures (few typos corrected, 3 references added, final version to appear in Nucl.Phys.B)

References in corpus (4)

• Nonlocal Yang-Mills
• Simplifications in Lagrangian BV quantization exemplified by the anomalies of chiral $W_3$ gravity
• Regularization Methods in Chiral Perturbation Theory
• Abelian Anomalies in Nonlocal Regularization

Cited by in corpus (15)

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• Perturbative Quantum Gravity on Complex Spacetime
• Higher Loop Anomalies and their Consistency Conditions in Nonlocal Regularization
• QFT with Stubs
• The BPHZ renormalised BV master equation and Two-loop Anomalies in Chiral Gravities
• A Superspace Formulation for the Master Equation
• Nonlocal regularization of abelian models with spontaneous symmetry breaking
• Superspace formulation of general massive gauge theories and geometric interpretation of mass-dependent BRST symmetries
• Superspace Formulation for the BRST Quantization of the Chiral Schwinger Model
• Global Anomalies in the Batalin Vilkovisky Quantization
• Quantum BRST operators in the extended BRST-anti-BRST formalism
• Axial Anomaly from the BPHZ regularized BV master equation
• On the determination of anomalies in supersymmetric theories
• The effect of different regulators in the non-local field-antifield quantization
• The SU(2) Skyrme model and anomaly