Conformal theories with an infrared cutoff

K.-I. Ishikawa, Y. Iwasaki, Yu Nakayama, and T. Yoshie Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan California Institute of Technology, Pasadena, California 91125, USA (Received 21 January 2013; published 30 April 2013) We give a new perspective on the dynamics of conformal theories realized in the SUðNÞ 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 IR, we conjecture that the propagator of a meson GHðtÞ on a lattice behaves at large t as a power-law corrected Yukawa-type decaying form GHðtÞ 1⁄4 ~ cH exp ð ~ mHtÞ=t H instead of the exponentially decaying form cH exp ð mHtÞ, in the small quark mass region where mH c IR: 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 1⁄4 7 case and the Nf 1⁄4 16 case in the SU(3) gauge theory with the fundamental representation.