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

Abstract

The observation that $SU(3)/SU(2)\ensuremath{\cong}{S}^{5}$ 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 $SU(3)\ifmmode\times\else\texttimes\fi{}SU(3)/SU(3)$. By reduction of $SU(3)\ifmmode\times\else\texttimes\fi{}U(1)/SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ to $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)/U(1)$, the construction gives a topological derivation of the WZW term for the standard model Higgs field.