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

Abstract

The observation that SU (3)/SU (2) ∼ = 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) × 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.

Gauged WZW Models via Equivariant Cohomology

“…Furthermore in Ref. [7] a topological derivation of the WZW term for the Standard Model Higgs field is obtained through an interesting symmetry breaking reduction.…”