A Renormalization Group Study of the $(ϕ^* ϕ)^3$ Model coupled to a Chern-Simons Field

Abstract

We consider the model of a massless charged scalar field, in (2+1) dimensions, with a self interaction of the form $lambda (ϕ^* ϕ)^3$ and interacting with a Chern Simons field. We calculate the renormalization group $β$ functions of the coupling constants and the anomalous dimensions $γ$ of the basic fields. We show that the interaction with the Chern Simons field implies in a $β_λ$ which suggests that a dynamical symmetry breakdown occurs. We also study the effect of the Chern Simons field on the anomalous dimensions of the composite operators $(ϕ^* ϕ)^n$, getting the result that their operator dimensions are lowered.