Four-fermion field theories and the Chern-Simons field: A renormalization group study (original) (raw)

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 α becomes bigger than a critical α c . Composite operators are also analyzed and it is shown that a specific four fermion interaction has an improved ultraviolet behavior as N increases. Fermionic quartic interactions have been very important for the clarification of conceptual aspects as well as for the applications of Quantum Field Theory. Illustrative examples of such dual role are provided by the Thirring and Nambu-Jona Lasinio models. However, perturbative studies of the models have been hampered by the fact that only in two dimensions they are renormalizable. If the number of flavors is high enough, a better ultraviolet behavior is achieved in the context of the 1/N expansion which turns out to be renormalizable up