Cartan gauge

The first choice is called the Cartan gauge the second one is the Pauli gauge (Altmann (1986), p. 108 see also Section 11.8). 

Gauging the Wess-Zumino term with to respect the electromagnetic interactions yields the familiar 7r° — 27 anomalous decay. This term [35] can be written compactly using the language of differential forms. It is useful to introduce the algebra-valued Maurer-Cartan one form a = a dx = (d U) U l dxF = (dU) U l which transforms only under the left SUp 3) flavor group. The Wess-Zumino effective action is... 

---