Sugawara Model and Goldstone Bosons

We find that neutral and $\mathrm{SU}\left(2\right)\mathrm{}$ [and consequently $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$] Sugawara current theories are completely equivalent to canonical Lagrangian field theories of massless scalar fields. A Sugawara current theory is obtained by eliminating all the massive fields in a theory of spontaneous symmetry breakdown and retaining the Goldstone bosons only. The reverse is also true in that all Abelian or $\mathrm{SU}\left(2\right)\mathrm{}$ Sugawara theories are necessarily equivalent to these canonical representations, so that for these groups "Sugawara physics" reduces simply to "Goldstone boson physics."