Asymptotic Conformal Invariance in a Non-Abelian Chern-Simons-Matter Model

TL;DR

This paper demonstrates that a non-Abelian SU(2) Chern-Simons-matter model maintains asymptotic conformal invariance at all perturbative orders, linking classical symmetry to quantum behavior through the Callan-Symanzik equation.

Contribution

It establishes the existence of solutions to the Callan-Symanzik equation showing asymptotic conformal invariance in a non-Abelian Chern-Simons-matter model at all orders.

Findings

Conformal symmetry holds classically via local criteria.

Asymptotic conformal invariance persists quantum mechanically.

Results extend to SU(n) models, with potential exceptions being accidental.

Abstract

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 $\beta$-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.