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.

在这个财政年度，我专注于两项主要的研究活动：（1）与合作者一起，我调查了扰动贡献引起的颜色限制的可能性。我们探索了在高温下使用假想的角速度的使用，从而导致连续连接到常规的非驱动限制相位的扰动相位相位，以及触觉扰动的反登录相变。这一发现建立了一个对限制物理学的扰动实验室，我们可以在其中研究许多与监禁相关的现象。（2）与合作者，我对拓扑孤子保护法的常规理解提出了质疑。虽然流行的观点是孤子对称性是由同质组决定的，但我们发现了更复杂的代数结构。我们发现线和点缺陷操作员之间的相关函数高度非常规选择规则。对此的孤子对称对称性不能像群体一样，而是不可固化的，并且取决于拓扑数据，而不是同型组。此外，它的可逆部分由一些广义的共同体学（例如bordism）决定，而不是同型组。这一发现还表明，孤子对称性在理解Abelian不可粘的对称性中的杰出作用，这可能打开了探究的新途径，并加深了我们对广义对称性的理解。