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Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter

The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved effective potential computation based on two-loop calculations and the renormalization group equation: the later allows us to sum up series of terms in the effective potential where the power of the logarithms are one, two and three units smaller than the total power of coupling constants (i.e., leading, next-to-leading and next-to-next-to-leading logarithms). For the sake of this calculation we determined the beta function of the fermion-fermion-scalar-scalar interaction and the anomalous dimension of the scalar field. We shown that the improved effective potential provides a much more precise determination of the properties of the theory in the broken phase, compared to the standard effective potential obtained directly from the loop calculations. This happens because the region of the parameter space where dynamical symmetry breaking occurs is drastically reduced by the improvement discussed here.