  We give a new perspective on the dynamics of conformal theories realized in
the SU(N) gauge theory, when the number of flavors N_f is within the conformal
window. Motivated by the RG argument on conformal theories with a finite IR
cutoff \Lambda_{IR}, we conjecture that the propagator of a meson G_H(t) on a
lattice behaves at large t as a power-law corrected Yukawa-type decaying form
G_H(t) = c_H \exp{(-m_H t)}/t^{\alpha_H} instead of the exponentially decaying
form c_H\exp{(-m_H t)}, in the small quark mass region where m_H \le c
\Lambda_{IR}: m_H is the mass of the ground state hadron in the channel H and c
is a constant of order 1. The transition between the "conformal region" and the
"confining region" is a first order transition. Our numerical results verify
the predictions for the N_f=7 case and the N_f=16 case in the SU(3) gauge
theory with the fundamental representation.
