We give a new perspective on the dynamics of conformal theories realized in the $\mathrm{SU}(N)$ gauge theory, when the number of flavors $N_f$ is within the conformal window. Motivated by the renormalization group argument on conformal theories with a finite IR cutoff ${\Lambda }_{\mathrm{IR}}$, 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 $G_H(t)={\tilde{c}}_H\exp (-{\tilde{m}}_{H}t)/t^{{\alpha }_H}$ instead of the exponentially decaying form $c_H\exp (-m_{H}t)$, in the small quark mass region where $m_H\le c{\Lambda }_{\mathrm{IR}}$: $m_H$ 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.

• Received 21 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.071503