Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study

Details Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study

1999-04-20

arxiv.org/abs/hep-th/9904139v1

Phys.Rev. D60 (1999) 027701

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, revtex

Scientific paper

10.1103/PhysRevD.60.027701

In (2+1) dimensions, we consider the model of a $N$ flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and Thirring like terms. The four fermion interaction is not perturbatively renormalizable and the model is taken as an effective field theory in the region of low momenta. Using Zimmerman procedure for reducing coupling constants, it is verified that, for small values of the Chern-Simons parameter, the origin is an infrared stable fixed point but changes to ultraviolet stable as $\alpha$ becomes bigger than a critical $\alpha_c$. Composite operators are also analyzed and it is shown that a specific four fermion interaction has an improved ultraviolet behavior as $N$ increases.

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