Simplifications in Lagrangian BV quantization exemplified by the anomalies of chiral $W_3$ gravity

Abstract

The Batalin--Vilkovisky (BV) formalism is a useful framework to study gauge theories. We summarize a simple procedure to find a a gauge--fixed action in this language and a way to obtain one--loop anomalies. Calculations involving the antifields can be greatly simplified by using a theorem on the antibracket cohomology. The latter is based on properties of a `Koszul--Tate differential', namely its acyclicity and nilpotency. We present a new proof for this acyclicity, respecting locality and covariance of the theory. This theorem then implies that consistent higher ghost terms in various expressions exist, and it avoids tedious calculations. This is illustrated in chiral $W_3$ gravity. We compute the one--loop anomaly without terms of negative ghost number. Then the mentioned theorem and the consistency condition imply that the full anomaly is determined up to local counterterms. Finally we show how to implement background charges into the BV language in order to cancel the anomaly with the appropriate counterterms. Again we use the theorem to simplify the calculations, which agree with previous results.

45 pages

References in corpus (7)

• Geometry of Batalin-Vilkovisky quantization
• Special geometry, cubic polynomials and homogeneous quaternionic spaces
• Trace Anomalies from Quantum Mechanics
• A Derivation of the BRST Operator for Non-Critical W-Strings
• Hiding Anomalies
• The regularized BRST Jacobian of pure Yang-Mills theory
• Nonlocal regularisation and two-dimensional induced actions

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• Koszul-Tate Cohomology For an Sp(2)-Covariant Quantization of Gauge Theories with Linearly Dependent Generators
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