Renormalization group study of the (φ*φ)3 model coupled to a Chern-Simons field

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