0 v 1 5 J ul 1 99 4 UdeM - LPN - TH - 94 - 202 hep - th / 9407030 RADIATIVE CORRECTIONS IN NONRELATIVISTIC CHERN - SIMONS THEORY

We present the one-loop scalar field effective potential for the N = 2 supersymmetric nonrelativistic self-interacting matter fields coupled to an Abelian Chern-Simons gauge field and for its generalization when bosonic matter fields are coupled to non-Abelian Chern-Simons field. In both models, Gauss’s law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. We compute the scalar field effective potentials in two gauge families, a gauge reminiscent of the Rξ-gauge in the limit ξ → 0 and in the Coulomb family gauges. We regularize the theory with operator regularization and a cutoff to demonstrate that the results are independent of the regularization scheme. 1. The models. 1.1. N = 2 supersymmetric nonrelativistic Chern-Simons model The first model we consider is composed of self-interacting scalar field and fermionic field coupled to an Abelian Chern-Simons gauge field 1 [diag η = (+,−,−)]