119222022
Conformal Behavior in QCD
AbstractWe give a new perspective on the properties of quarks and gluons at nite temperature T in N f = 2 ˘6 QCD. Wepoint out the existence of an IR xed point for the gauge coupling constant at T>T c (T c is the chiral phase transitiontemperature). Based on this observation we predict theoretically that the propagators of a meson G H (t) at T=T c >1decay with a power-law corrected Yukawa-type decaying form, G H (t) = cexp( m~ H t)=t , instead of the exponentiallydecaying form c H exp( m H t), in the "conformal region" de ned by m H <c IR , where IR is the IR cuto , m H ;m~ H are characteristic scales of the spectrum in the cannel H and cis a constant of order 1. The decaying form is thecharacteristics of conformal theories with an IR cuto . This prediction is also applicable to any QCD with compactspace in the decon ning region. We verify numerically the conjecture on a lattice with size 16 3 64. We discuss in detailhow the resulting hyper-scaling relation of physical observables may modify the existing argument about the order ofthe chiral phase transition in the N
118596659
Global Structure of Conformal Theories in the SU(3) Gauge Theory
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 "local analysis", we conjecture that the "conformal region" exists together with the confining region and the deconfining region in the phase structure parametrized by beta 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 as High Temperature QCD). 
Our numerical simulation on a lattice of the size 16^3 x 64 shows the following evidence of the conjecture. In the conformal region we find the vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative effects and temporal propagators of meson 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 in High Temperature QCD. 
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. In particular, we find the correspondence between Conformal QCD with Nf = 7 and High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson unparticle model. From this we estimate the anomalous mass dimension gamma* = 1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc --> infty is a free quark state in the Z(3) twisted vacuum.
15591179
Scaling of Chiral Order Parameter in Two-Flavor QCD
The finite temperature transition of QCD with two degenerate light quarks is studied on the lattice with a renormalization group improved gauge action and the Wilson quark action. We have made simulations on an 8{sup 3}{times}4 lattice near the chiral transition point. It is shown that the chiral condensate, which is the order parameter of chiral symmetry, satisfies remarkably a scaling relation with the exponents of the three-dimensional O(4) Heisenberg model. This indicates that the chiral transition in two-flavor QCD is of second order in the continuum limit. {copyright} {ital 1997} {ital The American Physical Society}
118391216
Conformal Window and Correlation Functions in Lattice Conformal QCD
We discuss various aspects of Conformal Field Theories on the Lattice. We mainly investigate the SU(3) gauge theory with N_f 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 N_f 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 Lambda_{IR}. Then we make predictions that when N_f is within the conformal window, the propagator of a meson G(t) behaves at large t, as G(t) = c exp(-m_H t)/t^alpha, 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 N_f=7 case and the N_f=16 case. 
Thirdly, we discuss small number of flavors (N_f=2 sim 6) QCD at finite temperatures. We point out theoretically and verify numerically that the correlation functions at T/T_c > 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 N_f=7 case and the N_f=2 at T sim 2 T_c case are close to the meson unparticle model, and we estimate gamma^* = 1.2(1). On the other hand, the N_f=16 case and the N_f=2 at T= 10^2 sim 10^5 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.
6302391
Phase structure of lattice QCD for general number of flavors
We investigate the phase structure of lattice QCD for general number of flavors $N_F$. Based on numerical results combined with the result of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only a trivial fixed point and therefore the theory in the continuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial fixed point and therefore the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$.
118477010
Renormalization Group Analysis of Lattice Theories and Improved Lattice Action. II -- four-dimensional non-abelian SU(N) gauge model
A new block spin renormalization group transformation for SU(N) gauge models is proposed near the non-trivial fixed point in perturbation theory and thereby the expectation values of various Wilson loops on the renormalized trajectory near the fixed point are explicitly obtained. An improved action is obtained as in a preceding paper and a criterion for the scaling behavior of physical quantities is also given.
14077627
Vacuum Effects and Compressional Properties of Nuclear Matter in Cutoff Field Theory
Including the vacuum effects, the compressional properties of nuclear matter are studied in the cutoff field theory. Under the Hartree approximation, the low-energy effective Lagrangian is derived in the framework of the renormalization group methods. The coefficients are determined in a way where the physical results hardly depend on the value of the cutoff which is conveniently introduced into the theory. It is shown that, to reproduce the empirical data of the nucleus incompressibility, the compressibility of the nuclear matter is favorable to be 250$\sim$350MeV.