近日，巴西圣保罗大学L. A. Ferreira团队研究了（3+1）维杨-米尔斯理论的隐对称性。该项研究成果发表在2025年11月18日出版的《高能物理杂志》上。
研究组证明了在（3+1）维闵可夫斯基时空中，与自旋1/2及自旋0基本物质场耦合的经典非超对称杨-米尔斯理论，具有类可积结构的精确特性——存在无穷多个对易守恒荷。这类结构存在于非阿贝尔电荷与磁荷的承载空间中，以广义环路空间中的平坦联络为基础，并呈现出R-矩阵与Sklyanin关系。
研究组提出了杨-米尔斯理论的两种新颖对称性：其一对应于由泊松括号下无穷守恒荷生成的全局变换，规范场与物质场以及Wilson线、通量场在此全局对称下均展现有趣的变换规律；其二对应于导出守恒荷的杨-米尔斯积分方程对称性，这些对称性生成无限维群，其元素为从圆环S1到场空间的函数环路空间上连接的完整集。该方法完全适用于基本相互作用的标准模型。这些守恒荷具有规范不变性，因此在QCD情形下，它们作为色单态或许不受禁闭效应影响，强子可能携带此类荷。该研究为构建杨-米尔斯理论的非微扰方法开辟了新路径。
附：英文原文
Title: The hidden symmetries of Yang-Mills theory in (3 + 1)-dimensions
Author: Ferreira, L. A., Malavazzi, H.
Issue&Volume: 2025-11-18
Abstract: We show that classical, non-supersymmetric Yang-Mills theories coupled to spin-1/2 and spin-0 elementary matter fields, in (3 + 1)-dimensional Minkowski space-time, possess exact structures that resemble integrability, with an infinite number of conserved charges in involution. Such structures live in the space of non-abelian electric and magnetic charges, and are based on flat connections in generalized loop spaces, presenting an R-matrix, and Sklyanin relation. We present two novel symmetries of Yang-Mills theories. The first one corresponds to global transformations generated by the infinity of those conserved charges under the Poisson brackets. The gauge and matter fields, as well as Wilson lines and fluxes, have interesting transformation laws under such a global symmetry. The second one corresponds to symmetries of the integral Yang-Mills equations, which lead to the conserved charges. They generate an infinite-dimensional group, where the elements are holonomies of connections on the loop space of functions from the circle S1 to the space-time. Our approach certainly applies to the Standard Model of the Fundamental Interactions. The conserved charges are gauge invariant, and so, in the case of QCD, they are color singlets and perhaps are not confined. Therefore, the hadrons may carry such charges. Our results open up the way for the construction of non-perturbative methods for Yang-Mills theories.
DOI: 10.1007/JHEP11(2025)102
Source: https://link.springer.com/article/10.1007/JHEP11(2025)102