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Analytic approach to nonperturbative aspects of gauge theories

规范理论非微扰方面的分析方法

基本信息

批准号：
13135203
负责人：
FUJIWARA Takanori
金额：
$ 4.22万
依托单位：
Ibaraki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13135203/
关键词：
gauge theory lattice gauge theory chiral anomaly effective field theory confinement index theorem topological charge regularization gauge field lattice gauge theory chiral anomaly Dirac operator lattice fermion magnetic monopole

项目摘要

To have better understandings about nonperturbative aspects of guage field theories such as topological structure, constructive formulation, supersymmetry and quark confimenent it is helpful to develop analytical methods such as lattice gauge theory and effective field theory approaches.In lattice gauge theory approach we investigated chiral gauge theories based on lattice Dirac operator satisfying the Ginsparg-Wilson relation and made it clear the topological structure of lattice gauge fields (Fujiwara). Furthermore, we developeded a cohomological method to classify topological invariants. This tourned out to be useful to facilitate construction of chiral U(1) gauge theories on the lattice. Furthermore, we gave a concrete construction of the fermion measure for SU(2)xU(1) electroweak gauge theory on the lattice (Kikukawa). We also investigated lattice regularization of supersymmetric gauge theories and gave a lattice formulation of N=(2, 2) supersymmetric Yang-Mills theory in lower dimensions (Suzuki).The topological structure of abelian gauge theories on a periodic lattice can be understood from abelian gauge theory on a torus. We investigated Dirac operator zero-modes on a torus with a uniform magnetic background in arbitrary even dimensions (Fujiwara). The twisted boundary conditions for the wave functions can be resolved by making use of the geometric nature of the torus. The eigenvalue problem can be solved completely. We found that a set of zero-mode with a desired chirality appear and the degeneracy of the zero-modes can be understood from the magnetic translation symmetry of the background gauge field. Our results are perfectly consistent with the index theorem.In effective field theory approach we investigated Cho-Faddeev-Niemi decomposition of Yang-Mills fields and explained the mechanism of quark confinement by reformulating the theory in terms of the nonlinear field transformations (Kondo).

为了更好地理解语言场理论的非微扰方面，如拓扑结构、构造公式、超对称和夸克确证，有助于发展晶格规范理论和有效场论方法等分析方法。在点阵规范理论方法中，我们研究了基于满足Ginsparg-Wilson关系的点阵Dirac算子的手性规范理论，明确了点阵规范场的拓扑结构（Fujiwara）。此外，我们发展了一种上同调方法来分类拓扑不变量。结果证明，这有助于在晶格上建立手性U(1)规范理论。此外，我们给出了晶格上SU(2)xU(1)电弱规范理论的费米子测度的具体构造。我们还研究了超对称规范理论的晶格正则化，并给出了低维N=(2,2)超对称Yang-Mills理论的晶格形式（Suzuki）。周期格上的阿贝尔规范理论的拓扑结构可以用环面上的阿贝尔规范理论来理解。我们研究了任意偶数维均匀磁背景环面上的Dirac算子零模。利用环面的几何性质，可以解决波函数的扭曲边界条件。特征值问题可以完全解决。我们发现存在一组具有期望手性的零模，并且零模的简并性可以从背景规范场的磁平移对称性来理解。我们的结果与指标定理完全一致。在有效场论方法中，我们研究了Yang-Mills场的Cho-Faddeev-Niemi分解，并通过非线性场变换重新阐述了夸克约束的机制（Kondo）。