Supersymmetry by lattice fermions near the continuum limit

点击翻译按钮获取中文摘要

In order to acquire deeper knowledge for the standard model of particle physics, lattice supersymmetry becomes a powerful tool but many difficulties exist. Even if the supersymmetry is realized, we must take a continuum limit for the lattice field theory because our world is considered as a continuous manifold. In the term of this grant, I and other investigators tried to define supersymmetry on lattice and to calculate its nonperturbative effects. Our results are classified into the following three parts ;(1) Symmetry Realization on Lattice Field Theories (Quantum Master Equation)Generally, regularized theories such as lattice theories have less symmetry than original one. We clarified that a new realization appears for the symmetry instead of loss of the symmetry. A quantum master equation controls the newly realized symmetry.(2) Ichimatsu Lattice and Exact Fermionic SymmetryWe proposed a new lattice pattern with mod 2 translational symmetry which is called Ichimatsu lattice. It is surprising that we found the exact fermionic symmetry on the lattice and the symmetry survives after the naive continuum limit. This symmetry is pre-realized under finite lattice constant before the real supersymmetry. Also some numerical analyses are studied.(3) Application to Microscopic ModelsAlthough it is generally difficult to find some explicit evidences, it may smart to investigate the effects on many Yukawa coupling constants. My investigator and his collaborators analyzed based on superconformal models. They showed that realistic Yukawa coupling constants is possible in this superconformal models.