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

V. S. Alves·M. Gomes·S. L. V. Pinheiro·A. J. da Silva
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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.

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V. S. Alves, M. Gomes, S. L. V. Pinheiro, A. J. da Silva. 2000-01-31. A Renormalization Group Study of the $(ϕ^* ϕ)^3$ Model coupled to a Chern-Simons Field. https://doi.org/10.1103/physrevd.61.065003

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