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アノマリーマッチングに基づくゲージ理論と相構造の非摂動的研究

基于异常匹配的规范理论与相结构非微扰研究

基本信息

批准号：
22KJ0599
负责人：
陳実
金额：
$ 1.41万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2023
资助国家：
日本
起止时间：
2023-03-08 至 2024-03-31
项目状态：
已结题

项目摘要

During this fiscal year, I focused on two main research activities:(1) With collaborators, I investigated the possibility of color confinement resulting from perturbative contributions. We explored the use of an imaginary angular velocity at a high temperature, which led to a perturbatively confined phase continuously connected to the conventional nonperturbative confined phase, as well as a perturbative deconfinement-confinement phase transition. This discovery establishes a perturbative laboratory for confinement physics where we can investigate many confinement-related phenomena perturbatively.(2) With collaborators, I challenged the conventional understanding of the conservation law of topological solitons. While the prevailing view is that solitonic symmetry is determined by homotopy groups, we discovered a far more sophisticated algebraic structure. We found a highly unconventional selection rule for the correlation function between line and point defect operators. Solitonic symmetry accounting for this cannot be group-like but non-invertible and depends on far finer topological data than homotopy groups. Besides, its invertible part is determined by some generalized cohomology like bordism, still instead of homotopy groups. This discovery also suggests a distinguished role of solitonic symmetry in understanding Abelian non-invertible symmetry, which may open up new avenues of inquiry and deepen our understanding of generalized symmetry.

在本财政年度，我集中在两个主要的研究活动：（1）与合作者，我调查了颜色禁闭的可能性，从微扰的贡献。我们探讨了在高温下使用的虚角速度，这导致了一个微扰约束相连续连接到传统的非微扰约束相，以及微扰解约束约束相变。这一发现为禁闭物理学建立了微扰实验室，在那里我们可以微扰地研究许多与禁闭相关的现象。(2)与合作者一起，我挑战了拓扑孤子守恒定律的传统理解。虽然主流观点认为孤子对称性是由同伦群决定的，但我们发现了一个复杂得多的代数结构。我们发现了一个非常非常规的选择规则之间的相关函数线和点缺陷运营商。解释这一点的孤子对称性不可能是类群的，而是不可逆的，并且依赖于比同伦群更精细的拓扑数据。此外，它的可逆部分仍然不是由同伦群确定的，而是由某些广义上同调如配边确定的。这一发现也表明了孤子对称性在理解阿贝尔不可逆对称性方面的杰出作用，这可能会开辟新的探索途径，加深我们对广义对称性的理解。