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

TL;DR

This paper presents a simple, quantized topological Wess-Zumino-Witten (WZW) term for the SU(3)/SU(2) coset, relevant for anomaly cancellation in Standard Model extensions, with a closed form and connections to other WZW terms.

Contribution

It introduces a straightforward WZW action for SU(3)/SU(2), providing a topological derivation and explicit coupling to gauge fields, enhancing understanding of anomaly cancellation.

Findings

Derived a closed form for the SU(3)/SU(2) WZW term.

Showed equivalence to a limit of the SU(3) x SU(3)/SU(3) WZW term.

Connected the construction to the Standard Model Higgs field WZW 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) x SU(3) / SU(3). By reduction of SU(3) x U(1) / SU(2) x U(1) to SU(2) x U(1) / U(1), the construction gives a topological derivation of the WZW term for the Standard Model Higgs field.