近日，英国伦敦帝国理工学院Hull, C. M.团队研究了单极子，狄拉克弦和广义对称性。相关论文于2025年9月1日发表在《高能物理杂志》上。

狄拉克的磁单极子公式被证明与麦克斯韦理论耦合到2型规范场是等价的，因此它具有局部1型对称性，2型规范场是由与狄拉克弦相关的2型电流密度给出的。狄拉克理论的场方程不依赖于狄拉克弦的位置，只要它们不与任何带电粒子的世界线相交；这种约束被称为狄拉克否决。

研究组证明了狄拉克作用与狄拉克弦的位置无关，这与局部1型对称相对应。电和磁的1-形式对称具有混合异常，并且狄拉克否决显示对应于对异常消失的规范变换的限制。研究组讨论了耦合到带电膜的d维p形规范场的扩展，以及通过嵌入高维理论来消除异常从而避免否决的可能性。

附：英文原文

Title: Monopoles, Dirac strings and generalised symmetries

Author: Hull, C. M.

Issue&Volume: 2025-09-01

Abstract: Dirac’s formulation of magnetic monopoles is shown to be equivalent to Maxwell theory coupled to 2-form gauge fields so that it has a local 1-form symmetry, with the 2-form gauge fields given in terms of the 2-form current densities associated with the Dirac strings. The field equations of Dirac’s theory do not depend on the positions of the Dirac strings provided that they do not intersect the worldlines of any electrically charged particles; this constraint is called the Dirac veto. It is shown that Dirac’s action is independent of the positions of the Dirac strings and that this corresponds to a local 1-form symmetry. The electric and magnetic 1-form symmetries have a mixed anomaly, and the Dirac veto is shown to correspond to a restriction to gauge transformations for which the anomaly vanishes. The extension to p-form gauge fields in d-dimensions coupled to charged branes is discussed, together with the possibility of cancelling the anomaly by embedding in a higher-dimensional theory and so avoiding the veto.

DOI: 10.1007/JHEP09(2025)019

Source: https://link.springer.com/article/10.1007/JHEP09(2025)019