2013/10/31 by Ken-Ichi Ishikawa, K. -I. Ishikawa, Y. Iwasaki +3 · 1 citation
Physics and Astronomy · #Combinatorics #Conformal map #Conjecture #Fermion #Geometry #High-Energy Particle Collisions Research #Lattice (music) #Lattice QCD #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.89.114503
published as Phys. Rev. D 89, 114503 (2014) · 48 pages, 47 figures and 7tables; two subsections added on "in relation to mass deformed CFT" and "finite size scaling"; a version to be published in PRD
arxiv created 2014/05/16 · openalex publication_date 2014/06/09 · arxiv updated 2014/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using a new method that we call ``local analysis,'' we conjecture that the ``conformal region'' exists together with the confining region and the deconfining region in the phase structure parametrized by \ensuremathβ and K, both in the cases of the large Nf QCD within the conformal window (referred as conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the chiral transition temperature (referred to as high-temperature QCD). Our numerical simulation on a lattice of the size 163\ifmmode×\else\texttimes\fi64 shows the following evidence of the conjecture. In the conformal region, we find that the vacuum is the nontrivial Z(3) twisted vacuum modified by nonperturbative effects and that temporal propagators of mesons behave at large t as a power-law-corrected Yukawa-type decaying form. The transition from the conformal region to the deconfining region or the confining region is a sharp transition between different vacua, and therefore, it suggests a first-order transition both in conformal QCD and high-temperature QCD. To confirm the conjecture and distinguish it from the possibility of crossover phenomena, we need to take the continuum/thermodynamic limit, which we do not attempt in this work. Within our fixed-lattice simulation, we find that there is a precise correspondence between conformal QCD and high-temperature QCD in the temporal propagators under the change of the parameters Nf and T/Tc, respectively: one boundary is close to meson states, and the other is close to free quark states. In particular, conformal QCD with Nf=7 corresponds to high-temperature QCD with Nf=2 at T\ensuremath∼2Tc, both of which are in close relation to a meson unparticle model. From this, we estimate the anomalous mass dimension \ensuremathγ*=1.2(1) for Nf=7. We also show that the asymptotic state in the limit T/Tc\ensuremath→\ensuremath∞ is a free quark state in the Z(3) twisted vacuum. The approach to a free quark state is very slow; even at T/Tc\ensuremath∼105, the state is affected by nonperturbative effects. This is possibly connected with the slow approach of the free energy to the Stefan-Boltzmann ideal gas limit.