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

TL;DR

This paper investigates a (2+1)-dimensional scalar field model coupled with a Chern-Simons field, analyzing its renormalization group flow, symmetry breaking, and operator dimensions to understand its quantum behavior.

Contribution

It provides a detailed renormalization group analysis of the scalar-Chern-Simons model, revealing effects on symmetry and operator dimensions not previously characterized.

Findings

Interaction with Chern-Simons field suggests dynamical symmetry breakdown.

Chern-Simons coupling lowers the anomalous dimensions of composite operators.

The model's beta functions indicate non-trivial fixed points and phase structure.

Abstract

We consider the model of a massless charged scalar field, in (2+1) dimensions, with a self interaction of the form $lambda (\phi^* \phi)^3$ and interacting with a Chern Simons field. We calculate the renormalization group $\beta$ functions of the coupling constants and the anomalous dimensions $\gamma$ of the basic fields. We show that the interaction with the Chern Simons field implies in a $\beta_{\lambda}$ 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 $(\phi^* \phi)^n$, getting the result that their operator dimensions are lowered.