## Numerical simulations of lattice gauge theories are performed aiming for detailed studies of the standard model of elementary particle physics and search for physics beyond the standard model.

QCD (quantum Chromodynamics) describes the strong interaction between quarks which are elementary particles constructing hadrons such as protons and neutrons. Nuclear force inside atomic nuclei is modeled by an effective theory of QCD. Characteristic feature of QCD is that the coupling increases as the distance between quarks. Thus analytic calculation based on the perturbation theory that is an expansion in coupling, applies only at high energy (short distance) and does not work at low energy. To investigate the hadron properties and their matrix elements quantitatively, therefore, one needs nonperturbative method.

Lattice gauge theory provides a framework to enable such studies. It is a field theory formulated in descretized four-dimensional Euclidean space-time, namely on a lattice. After path integral quantization, numerical calculation of physical observables becomes possible by Monte Carlo simulations. Thus lattice QCD simulations enable quantitative investigation of QCD in model independent way.

We are studying the following subjects:

(1) Large-scale numerical simulations with chirally symmetric fermion formulation.

(2) Analysis of gauge theories towards search for physics beyond the standard model.

(3) Studies of algorithms and numerical methods for computational

science.

Recent progress of theoretical understanding, development of architecture, improved algorithms has increased the precision and reliability of lattice QCD simulations. Simulation at physical point, namely with real up, down and strange quark masses as dynamical degrees of freedom, has become possible and applied to precise computation of hadronic matrix elements.

These simulations generate data called `gauge configurations', from which one can extract various physical quantities, while they require large numerical cost to generate. To fully make use of them, an international activity has developed a data grid to publicly share the gauge configuration that was named 'International Lattice Data grid' (ILDG) and started service in 2006.

Lattice gauge field theory is applied to not only QCD but also similar field theories. Recently lattice simulations have been applied to studies of physics beyond the standard model, such as supersymmetry and techinicolor theories.