Conformal dynamics in gauge theories via non-perturbative renormalization group

The dynamics at the IR fixed point realized in the $SU(N_c)$ gauge theories with massless Dirac fermions is studied by means of the non-perturbative renormalization group. The analysis includes the IR fixed points with non-trivial Yukawa couplings. The renormalization properties of the scalar field are also discussed and it is shown that hierarchical mass scale may be allowed without intense fine-tuning due to a large anomalous dimension.