Towards A New Formulation of Unified Model with Gravity on a Lattice

格子上重力统一模型的新表述

• 批准号: 13640250
• 负责人: KAWAMOTO Noboru
• 金额: $ 2.37万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640250/
• 关键词: Quantum Gravity; Lattice Gravity; Supersymmetry on the Lattice; Twisted Supersymmetry; Topological Field Theory; Dirac-kahler Fermion; Quantum gravity; Super Yang-Mills; Lattice SUSY; Dirac-Kahler Fermion; 超対称ゲージ理論; ツイストされた超対称空間; N=2超対称性; 一般化

My research thema in this period can be classified into the following 4 categories :1)Continuation from the previous investigations.2)Fermion Formulation with Non-commutativity on a Lattice.3)A Proposal of New Superspace Formulation.4)Supersymmetry on a Lattice.1)Based on the generalized gauge theory formulation which we discovered, we applied a truncated version of generalized Yang-Mills theory with SU(2|1) gauge group and derived Weinberg-Salam model. Numerical evaluation of the c-dependence of the fractal dimension of two-dimensional quantum surface was investigated and the result is perfect agreement with the analytic result which we obtained previously.2)We may introduce mild non-commutativity for the lattice difference operator tosatisfy the Leibniz rule. We can then define differential form on a lattice and introduce associative Clifford product. We have clarified the Dirac-Kahler fermion formulation with non-commutativity on a lattice.3)It was already recognized that the twisting appeared in the quantization of topological field theory can be identified as a Dirac-Kahler fermion formulation. We found that this twisting mechanism is a universal characteristic which appears in the quantization of topological field theory and a twisted superspace formulation is hidden behind the formulation. N=2 twisted superspace formulation was formulated in two dimensions. Then this formulation is extended into N=4 in four dimensions.4)Twisted superspace formulation is successfully formulated on a lattice with the introduction of the mild non-commutatibity for N=2 twisted superspace in two dimensions. It is now possible to apply this formulation to N=2 super Yang-Mills action on a lattice.

我这一时期的研究主题可以分为以下四类：1）先前研究的延续。2）格子上非交换性的费米子公式。3）新超空间公式的提议。4）格子上的超对称性.1)基于我们发现的广义规范理论公式，我们应用了具有SU(2|1)规范群的广义杨-米尔斯理论的截断版本并导出温伯格-萨拉姆模型。研究了二维量子表面分形维数的c依赖性的数值计算，结果与我们之前得到的解析结果完全一致。2）我们可以为晶格差分算子引入温和的非交换性以满足莱布尼茨法则。然后我们可以在格上定义微分形式并引入关联克利福德积。我们阐明了在格子上具有非交换性的Dirac-Kahler费米子公式。3)人们已经认识到拓扑场论量子化中出现的扭曲可以被识别为Dirac-Kahler费米子公式。我们发现这种扭曲机制是拓扑场论量子化中出现的普遍特征，并且其背后隐藏着一个扭曲的超空间公式。 N=2 扭曲超空间公式是在二维中制定的。然后将该公式推广到四个维度上的N=4。4)通过引入二维N=2扭曲超空间的温和不可交换性，在格子上成功地制定了扭曲超空间公式。现在可以将此公式应用于晶格上的 N=2 超杨-米尔斯作用。