Anomalies and Wess-Zumino Terms in an Extended, Regularized Field-Antifield Formalism

TL;DR

This paper advances the quantization of anomalous gauge theories within the extended Field-Antifield formalism, utilizing Pauli-Villars regularization to analyze anomalies, incorporate quantum effects, and interpret the Wess-Zumino action, with applications to the bosonic string.

Contribution

It introduces a PV regularization approach that simplifies anomaly expressions and extends the formalism to include quantum effects of extra variables, offering a new perspective on the Wess-Zumino action.

Findings

Derived an alternative anomaly expression involving only the regulator.

Showed nontrivial antifield-dependent cocycles do not appear in PV regularization.

Reproduced the Liouville action and the shift (26-D)→(25-D) at one loop for the bosonic string.

Abstract

Quantization of anomalous gauge theories with closed, irreducible gauge algebra within the extended Field-Antifield formalism is further pursued. Using a Pauli-Villars (PV) regularization of the generating functional at one loop level, an alternative form for the anomaly is found which involves only the regulator. The analysis of this expression allows to conclude that recently found ghost number one cocycles with nontrivial antifield dependence can not appear in PV regularization. Afterwards, the extended Field-Antifield formalism is further completed by incorporating quantum effects of the extra variables, i.e., by explicitly taking into account the regularization of the extra sector. In this context, invariant PV regulators are constructed from non-invariant ones, leading to an alternative interpretation of the Wess-Zumino action as the local counterterm relating invariant and non-invariant regularizations. Finally, application of the above ideas to the bosonic string reproduces the well-known Liouville action and the shift $(26-D)\rightarrow(25-D)$ at one loop.