ChiralSU4⊗SU4and scale invariance

Abstract

Proceeding from the speculation that the real world is approximately ${\mathrm{SU}}_4\otimes {\mathrm{SU}}_{4^{-}}$ and scale-invariant, we study the mechanism of spontaneous breakdown by considering a $\sigma$-type model that embodies both operator partial conservation of axial-vector current and operator partial conservation of dilatation current. Solutions exhibiting spontaneous breakdown are analyzed in relation to the behavior of transition when explicit symmetry breaking is turned on. Allowed domains for the symmetry-breaking parameters are also derived.