ON THE GAUGE INVARIANCE OF WESS–ZUMINO–WITTEN EFFECTIVE ACTION

It is shown that in order to introduce the gauge invariant Wess-Zumino-Witten effective action a global anomalyfree condition should be satisfied by the gauged subgroup of SU(3)_L × SU(3)_R. The condition requires that the left handed and the right handed Chern-Simons 5-forms with respect to the gauge group be equal to each other and it turns out in the local sense to be the usual perturbative anomaly-free condition. It is also constructed a gauge invariant effective action under the anomaly-free condition by means of a systematic method rather than the trial and error Noether method. In the non-abelian case, the gauge invariant effective action presented here contains less terms than the one obtained by Witten. The case of pure gauge is discussed in the present note as well.