权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Study of supersymmetric non-linear sigma models

超对称非线性sigma模型的研究

基本信息

批准号：
13640283
负责人：
HIGASHIJIMA Kiyoshi
金额：
$ 1.41万
依托单位：
Osaka 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 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640283/
关键词：
Non-linear sigma model renormalization group Ricci-flat manifold auxiliary field formulation large N method Einstein-Kahler manifold 超対称性非線形シグマ模型くりこみ群 Ricci Flat manifold 補助場の方法 Large N

项目摘要

Study of non-linear sigma models is important for several reasons. Two-dimensional non-linear sigma models describe propagation of strings in vurved space-time. It is also a gymnasium for non-perturbative study of difficult phenomena in field theories, like mass generation, bound states problem, dynamical symmetry breaking. It also offers an example of a possible renormalizable field theory that is not renormalizable in perturbation theory. In this project, we proposedA)Auxiliary field formulation of non-linear sigma models with N=2 supersymmetry.B)Non-perturbative study of N=2 supersymmetric non-linear sigma models by using the above methodC)Search of conformal field theories by using the renormalization group equation.D)Study of conformally invariant non-linear sigma models on non-compact manifolds.We successfully formulated N=2 supersymmetric non-linear sigma models on hermitian symmetric spaces by introducing both D-term and F-term constraints. We applied the large N method to study the non-perturbative phenomena in non-linear sigma models on CP^N and Q^N. We also obtained conformal field theories on non-compact Ricci-flat manifolds constructed as a line bundle Einstein-Kahler manifold. We derived the non-perturbative renormalization group equation for N=2 supersymmetric non-linear sigma models. By solving the fixed point equation, we found new conformal field theories with anomalous dimension.

非线性模型的研究很重要，原因有几个。二维非线性模型描述了弦在弯曲时空中的传播。它也是对质量生成、束缚态问题、动力学对称性破缺等场论难题进行非摄动研究的场所。它还提供了一个在微扰理论中不可重整的可能重整场论的例子。在本项目中，我们提出了a) N=2超对称的非线性sigma模型的辅助场公式。B)利用上述方法研究N=2超对称非线性σ模型的非摄动研究c)利用重整化群方程寻找共形场理论。D)非紧流形上共形不变非线性σ模型的研究。通过引入d项和f项约束，我们成功地建立了厄米对称空间上N=2超对称非线性σ模型。应用大N方法研究了CP^N和Q^N非线性σ模型中的非摄动现象。我们还得到了用线束爱因斯坦-卡勒流形构造的非紧Ricci-flat流形的共形场理论。我们导出了N=2超对称非线性σ模型的非微扰重整化群方程。通过求解不动点方程，得到了新的具有异常维数的共形场理论。