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.

在本财年中，我重点开展了两项主要研究活动：（1）与合作者一起，我研究了扰动贡献导致的颜色限制的可能性。我们探索了在高温下使用虚角速度，这导致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。这一发现为约束物理建立了一个微扰实验室，在这里我们可以微扰地研究许多与约束相关的现象。(2) 与合作者一起，我挑战了对拓扑孤子守恒定律的传统理解。虽然普遍的观点是孤子对称性是由同伦群决定的，但我们发现了一种更为复杂的代数结构。我们发现了线缺陷算子和点缺陷算子之间的相关函数的非常规选择规则。解释这一点的孤子对称性不能是类群的，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，它的可逆部分是由一些广义上同调（如边函数）决定的，而不是同伦群。这一发现还表明，孤子对称性在理解阿贝尔不可逆对称性中发挥着重要作用，这可能会开辟新的探究途径并加深我们对广义对称性的理解。