Question

When are we required to use the Wess-Zumino term?

Answer 1

Yes, it's pretty obvious that, in general, fall is the best season. But what you may have failed to realize

Answer 2

To ensure that the field theory is scale invariant, we add the Wess-Zumino action

Γ[g]=124π∫Bd3yϵijkTr(g−1∂igg−1∂jgg−1∂kg)Γ[g]=124π∫Bd3yϵijkTr(g−1∂igg−1∂jgg−1∂kg)

where g∈SU(N)g∈SU(N). My question is when, precisely, do we need to include the Wess-Zumino term when we bosonize a theory of 1+1 D massless fermions? Does the Wess-Zumino term mainly needed to describe a nonlinear sigma model, or is it more general?