We give a new perspective on the dynamics of conformal theories realized in the SU(N) gauge theory, when the number of flavors Nf is within the conformal window. Motivated by the renormalization group argument on conformal theories with a finite IR cutoff ΛIR, we conjecture that the propagator of a meson GH(t) on a lattice behaves at large t as a power-law corrected Yukawa-type decaying form GH(t)=c∼Hexp⁡(-m∼Ht)/tαH instead of the exponentially decaying form cHexp⁡(-mHt), in the small quark mass region where mH≤cΛIR: mH 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 Nf=7 case and the Nf=16 case in the SU(3) gauge theory with the fundamental representation.

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