On the SO(N) symmetry of the chiral SU(N) Yang--Mills model

TL;DR

This paper explores the quantization of the anomalous SU(N) Yang--Mills model while preserving SO(N) symmetry, revealing a Wess--Zumino action with enhanced symmetry properties and analyzing related anomalies and constraints.

Contribution

It demonstrates the possibility of maintaining SO(N) symmetry in the quantization of the anomalous SU(N) Yang--Mills model and expresses the Wess--Zumino action in terms of chiral fields in the homogeneous space.

Findings

Wess--Zumino action has SO(N) symmetry

Modified anomaly and constraints are explicitly calculated

Chiral fields are expressed in the space SU(N)/SO(N)

Abstract

The posibility of quantizing the anomalous $SU(N)$ Yang--Mills model preserving the symmetry under the orthogonal subgroup is indicated. The corresponding Wess--Zumino action (1-cocycle) possesses the additional $SO(N)$ symmetry and can be expressed in terms of chiral fields taking values in the homogeneous space $SU(N)/SO(N)$. The modified anomaly and the constraints commutator (2-cocycle) are calculated.