Abstract:
The CP-PACS project is a five year plan, which formally started in April 1992 and has been completed in March 1997, to develop a massively parallel computer for carrying out research in computational physics with primary emphasis on lattice QCD. The initial version of the CP-PACS computer with a theoretical peak speed of 307 GFLOPS with 1024 processors was completed in March 1996. The final version with a peak speed of 614 GFLOPS with 2048 processors was completed in September 1996, and has been in full operation since October 1996. We describe the architecture, the final specification, the hardware implementation, and the software of the CP-PACS computer. The CP-PACS has been used for hadron spectroscopy production runs since July 1996. The performance for lattice QCD applications and the LINPACK benchmark are given.

Abstract:
Phase diagram of QCD with Wilson fermions for various numbers of flavors $N_F$ is discussed. Our simulations mainly performed on a lattice with the temporal size $N_t =4$ indicate the following: The chiral phase transition is of first order when $3 \le N_F \le 6$, while it is continuous when $N_F=2$. For the realistic case of massless u and d quarks and the strange quark with $m_q = 150$ MeV, the phase transition is first order. The sharp transition in the intermediate mass region for $N_F=2$ at $N_t=4$ observed by the MILC group disappears when an RG improvement is made for the pure gauge action.

Abstract:
The CP-PACS computer with a peak speed of 300 Gflops was completed in March 1996 and has started to operate. We describe the final specification and the hardware implementation of the CP-PACS computer, and its performance for QCD codes. A plan of the grade-up of the computer scheduled for fall of 1996 is also given.

Abstract:
Parallel computers dedicated to lattice field theories are reviewed with emphasis on the three recent projects, the Teraflops project in the US, the CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new commercial parallel computers are also discussed. Recent development of semiconductor technologies is briefly surveyed in relation to possible approaches toward Teraflops computers.

Abstract:
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.

Abstract:
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 $N_F \le 6$.

Abstract:
The aim of the CP-PACS project was to develop a massively parallel computer for performing numerical research in computational physics with primary emphasis on lattice QCD. The CP-PACS computer with a peak speed of 614 GFLOPS with 2048 processors was completed in September 1996, and has been in full operation since October 1996. We present an overview of the CP-PACS project and describe characteristics of the CP-PACS computer. The CP-PACS has been mainly used for hadron spectroscopy studies in lattice QCD. Main results in lattice QCD simulations are given.

Abstract:
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.

Abstract:
We introduce a new concept "conformal theories with an IR cutoff", after pointing out that the following two categories in SU(3) gauge theories with fundamental N_f fermions possess an IR fixed point: Large N_f QCD with N_f in the conformal window (referred as Conformal QCD) and small N_f QCD with N_f out of the conformal window at temperature T/Tc > 1 (referred as High Temperature QCD). In the conformal theories with an IR cutoff there exists the "conformal region'" together with the confining region and the deconfining region. We verify numerically on a lattice of the size 16^3 x64 the existence of the conformal region and the non-trivial Z(3) structure of the vacuum and the Yukawa-type decay form of meson propagators in the conformal region. We stress that High Temperature QCD is intrinsically accompanied with an IR cutoff. Therefore the understanding the vacuum structure and the property of correlation functions is the key to resolve long standing issues in High Temperature QCD. We further argue that there is a precise correspondence between Conformal QCD and High Temperature QCD in the temporal propagators under the change of the parameters N_f and T/T_c respectively: the one boundary is close to meson states and the other is close to free quark states. In particular, we find the correspondence between Conformal QCD with N_f = 7 and High Temperature QCD with N_f=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 N_f=7.

Abstract:
We propose a new non-perturbative method to compute derivatives of gauge coupling constants with respect to anisotropic lattice spacings (anisotropy coefficients). Our method is based on a precise measurement of the finite temperature deconfining transition curve in the lattice coupling parameter space extended to anisotropic lattices by applying the spectral density method. We determine the anisotropy coefficients for the cases of SU(2) and SU(3) gauge theories. A longstanding problem, when one uses the perturbative anisotropy coefficients, is a non-vanishing pressure gap at the deconfining transition point in the SU(3) gauge theory. Using our non-perturbative anisotropy coefficients, we find that this problem is completely resolved.