ON THE GAUGE INVARIANCE AND ANOMALY-FREE CONIDITION OF THE WESS–ZUMINO–WITTEN EFFECTIVE ACTION

A global anomaly-free condition and a non-abelian gauge invariant Wess–Zumino–Witten effective action with less terms have been found by a systematical method rather than by trial and error. The condition requires the difference between the left-and right-handed Chern–Simon five-forms wrt the gauge group must vanish and it turns out to be the usual condition in the local sense.