Scale and conformal invariance in Chern-Simons-matter field theory

We study perturbative renormalization of Dsss3 Chern-Simons gauge theory coupled to scalar and fermionic matter. We show that in the non-Abelian case the coefficient of the Chern-Simons term has infinite renormalization and that both the matter and the non-Abelian gauge fields acquire nonvanishing anomalous dimensions at the two-loop level. However, the two-loop P function of the gauge coupling always vanishes, indicating that scale and conformal invariance survive quantization and infinite renormalization.