2012/12/18 by M. Iwasaki, Iwasaki, Y.
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #High-Energy Particle Collisions Research #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.1212.4343
openalex publication_date 2012/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss various aspects of Conformal Field Theories on the Lattice. We mainly investigate the SU(3) gauge theory with Nf degenerate fermions in the fundamental representation, employing the one-plaquette gauge action and the Wilson fermion action. First we make a brief review of our previous works and thereby clarify the reason why we conjecture that the conformal window is 7 le Nf le 16. Secondly, we introduce a new concept, "conformal theories with an IR cutoff" and point out that any numerical simulation on a lattice is bounded by an IR cutoff LambdaIR. Then we make predictions that when Nf is within the conformal window, the propagator of a meson G(t) behaves at large t, as G(t) = c exp(-mH t)/talpha, that is, a modified Yukawa-type decay form, instead of the usual exponential decay form in the small quark mass region. 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 sim 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 decay with power correction. Further, we observe our data are consistent with the picture that the Nf=7 case and the Nf=2 at T sim 2 Tc case are close to the meson unparticle model, and we estimate gamma^* = 1.2(1). On the other hand, the Nf=16 case and the Nf=2 at T= 102 sim 105 Tc cases are close to a free state in the Z(3) twisted vacuum. The results give clues for long standing issues such as slow approach of the free energy to the Stefan-Boltzmann ideal gas limit.