Anomalies and Wess-Zumino terms in an extended, regularized field-antifield formalism

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) → (25 − D) at one loop.

Antibracket, antifields and gauge-theory quantization

“…For sample computations using a method that retain antifields throughout the computation, see ref. [133,257]. Other useful results for anomaly calculations can be found in [251,78,75,133,162,193,14,64,195,257] and references therein.…”

“…(8.57) shows that if δR = [R, G] for some G then the anomaly vanishes, as a consequence of the cyclicity of the trace [133]. Formally, Eq.…”

“…Properties obeyed by Γ are the same as those obeyed by S. Therefore, one can define a BRST structure associated with Γ [133]. The BRST structure tensors are encoded in Γ and the relations among them are given by (Γ, Γ) = 0.…”

BRST quantization of anomalous gauge theories

“…It can be seen in references [7] and [12] that anomalies correspond to a violation of the master equation that can be put in the form:…”

“…Can we BRST quantize a theory in which the anomalies are still present ? One could follow the approach that anomalies are really canceled, as did Gomis and Paris [12] and impose the properness condition just on the quantum action. This corresponds to neglecting the new symmetries.…”