1212.4343 (Y. Iwasaki)

Conformal Window and Correlation Functions in Lattice Conformal QCD    [PDF]

Y. Iwasaki

We discuss various aspects of Conformal Field Theories on the Lattice. We investigate the SU(3) gauge theory with Nf fermions in the fundamental representation. First we make a brief review of our previous works on the phase structure of lattice gauge theories in terms of the gauge coupling constant and the quark mass. We thereby clarify the reason why we conjecture that the conformal window is 7 =< Nf =< 16. Secondly, we introduce a new concept, "conformal theories with IR cutoff" and point out that any numerical simulation on a lattice is bounded by an IR cutoff Lambda_(IR). Then we make predictions that when Nf is within the conformal window, the propagator of a meson G(t) behaves as G(t) = c exp(-m_H t)/t^alpha at large t, that is, a modified Yukawa-type damping form, instead of the usual exponential damping form exp(-m_H t), in the small quark mass region where m_H < c Lambda_(IR) is satisfied: m_H is a generic mass of a hadron such as the pion mass and c is a constant of order 1. This holds on an any lattice for any coupling constant g, as far as g is between 0 and g*, where g* is the IR fixed point. We verify that numerical results really satisfy the predictions for the Nf=7 case and the Nf=16 case. Thirdly, we discuss small number of flavors (Nf=2~6) QCD at finite temperatures. We point out theoretically and verify numerically that the correlation functions at T/Tc > 1 exhibit the characteristics of the conformal function with IR cutoff, an exponential damping with power correction. Investigating our numerical data by a new method, the "micro-analysis" of propagators, we observe that our data are consistent with the picture that the Nf=7 case and the Nf=2 at T ~ 2Tc case are close to the meson unparticle model. On the other hand, the Nf=16 case and the Nf=2 at T= 10^2 ~10^5 Tc cases are close to the fermion unparticle model.

View original: http://arxiv.org/abs/1212.4343