SU(3)/SU(2): The simplest Wess-Zumino-Witten term

The observation that SU(3)/SU(2)≅S5 implies the existence of a particularly simple quantized topological action, or Wess-Zumino-Witten (WZW) term. This action plays an important role in anomaly cancellation in extensions of the standard model electroweak sector. A closed form is presented for the action coupled to arbitrary gauge fields. The action is shown to be equivalent to a limit of the WZW term for SU(3)×SU(3)/SU(3). By reduction of SU(3)×U(1)/SU(2)×U(1) to SU(2)×U(1)/U(1), the construction gives a topological derivation of the WZW term for the standard model Higgs field.