SO(N) invariant Wess-Zumino action and its quantization

Abstract

A consistent quantization procedure of anomalous chiral models is discussed. It is based on the modification of the classical action by adding Wess-Zumino terms. The $SO(3)$ invariant WZ action for the $SO(3)$ model is constructed. Quantization of the corresponding modified theory is considered in details.Comment: 22 pages, LaTe

Local BRST cohomology of the gauged principal nonlinear sigma model

“…In particular, there is no perturbative anomaly. This provides a cohomological interpretation of the Wess-Zumino anomaly cancellation mechanism [11,12,43]. By enlarging the original field space with the group elements g (if the complete gauge group is broken), the anomaly becomes trivial, i.e.…”

On the canonical quantization of anomalousSu(N) chiral Yang-Mills models

“…But as was mentioned in the Introduction for some SU(N) groups this action can have degenerate symplectic form. This means that there are a number of additional primary constraints that can generate for example some secondary constraints and so on [14,15]. In this case one should modify the Faddeev-Shatashvili method to include the whole tower of the constraints.…”

“…Due to the fact that WZ action is the first order one in its fields the symplectic form must be degenerate at least for all odd-dimensional groups such as SU(2k), dim SU(2k) = 4k 2 − 1. The particular case of two dimensional SU(2) and four dimensional SU(3)/SO(3) models was considered in [14,15]. In this paper we consider the general case of SU(N) group with degenerate symplectic form in four space-time dimensions.…”

Nambu-Goldstone fields, anomalies and WZ terms

“…28) and the corresponding anti-fields. In terms of new variables, all b * terms cancel out and we obtainS = Ŝ + dx [ Θ * {∂ α Θ Cα − ∂ α Cα } + Θ ′ * b ],(3.29)where Ŝ is S in which all fields and anti-fields are replaced by corresponding new ones.…”

“…For YM type theories this possibility has been studied for example in[16][28] 4. The generalizations to reducible and on-shell theories may be examined by consulting[26].…”