Perfect action on the lattice

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Purpose of this investigation is to find lattice gauge actions which enable us to maake precise estimates for physical properties of strongly interacting elementary particles by numerical simulation. A basic idea for this investigation is to find a invariant action with respect to scale transformation. For this purpose, in 1995 and 1996, coupling flow and renormalized trajectory in 2-dmensional space (1x1 and 1x2 loop coupling) has been studied by blocking technique and Schwinger-Dyson method to determine renormalization effects to the couplings. As results of a series of numerical analysis, gross feature of coupling flow and a part of the renormalized trajectory has been clarified. In 1997, studies have been continued based on those results. In order to examine truncation effect on the 2-dimensional renormalization trajectory, flow analyzes have been made in 3-dimensional space where twist loop coupling has been included. It turned out that renormalization effect for twist coupling is … More small if flow starts near the 2-dimensional renormalization trajectory. This result has suggested that actions near the 2-dimensional renormalization trajectory is enough improved and practically useful one from a view point of computational cost. Restoration of rotational symmetry and week dependence of ratio of physical quantities on lattice constant were examined for the 2-loop coupling action near the renormalization trajectory. A preliminary study has indicated that the action shows much better restoration of rotational symmetry in comparison with Symanzik's action and Iwasaki's action as well as Wilson's one. As for the dependence of ratio between string tension and transition temperature squared, it is as good as Iwasaki's action. Further extensive examination will be required as the next step. A MPI (Message Passing Interface) program for gauge field generation on parallel processor has been developed in course of the investigation. It is designed for large scale lattice QCD simulation on currently available massively parallel computers. Less