Asymptotic conformal invariance in a non-Abelian Chern–Simons-matter model

One shows here the existence of solutions to the Callan–Symanzik equation for the non-Abelian SU(2) Chern–Simons-matter model which exhibits asymptotic conformal invariance to every order in perturbative theory. The conformal symmetry in the classical domain is shown to hold by means of a local criteria based on the trace of the energy–momentum tensor. By using the recently exhibited regimes for the dependence between the several couplings in which the set of β-functions vanish, the asymptotic conformal invariance of the model appears to be valid in the quantum domain. By considering the SU(n) case the possible non validity of the proof for a particular n would be merely accidental.