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Supersymmetry by lattice fermions near the continuum limit

接近连续极限的晶格费米子的超对称性

基本信息

批准号：
12640259
负责人：
SO Hiroto
金额：
$ 1.54万
依托单位：
NIIGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640259/
关键词：
Lattice Field Theory Supersymmetry Master Equation Continuum Limit 格子フェルミオン

项目摘要

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.

为了加深对粒子物理标准模型的认识，晶格超对称性成为一种强有力的工具，但也存在许多困难。即使超对称性被实现，我们也必须对格子场理论取一个连续极限，因为我们的世界被认为是一个连续的流形。在这项研究中，我和其他研究人员试图定义晶格上的超对称性，并计算它的非微扰效应。我们的结果分为以下三个部分：(1)晶格场理论(量子主方程)上的对称性实现一般而言，正则化理论，如晶格理论，比原来的理论具有更少的对称性。我们澄清了对称性的新实现，而不是对称性的丧失。新实现的对称性由量子主方程控制。(2)今松晶格与费米子精确对称性我们提出了一种新的具有mod 2平移对称性的晶格图案，称为今松晶格。令人惊讶的是，我们在晶格上发现了精确的费米子对称性，并且对称性在天真的连续统极限之后仍然存在。在真正的超对称之前，这种对称性是在有限晶格常数下预先实现的。(3)在微观模型中的应用虽然一般很难找到明确的证据，但研究它对许多Yukawa耦合常数的影响可能是明智的。我的研究人员和他的合作者基于超保角模型进行了分析。他们表明，在这种超保角模型中，现实的汤川耦合常数是可能的。