A Renormalization Group Study of the $({\varphi }^{\ast }\varphi {)}^3$ 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 $lambda({\varphi }^{\ast }\varphi {)}^3$ 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 $({\varphi }^{\ast }\varphi {)}^n$, getting the result that their operator dimensions are lowered.

21 pages (revtex), 11 figures (eps). To appear in Phys. Rev. D