Title: Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs Show Chinese title

Title: 随机三维杨-米尔斯-希格斯规范协变重整化的唯一性

Abstract: Local solutions to the 3D stochastic quantisation equations of Yang-Mills-Higgs were constructed in (arXiv:2201.03487), and it was shown that, in the limit of smooth mollifications, there exists a mass renormalisation of the Yang-Mills field such that the solution is gauge covariant. In this paper we prove uniqueness of the mass renormalisation that leads to gauge covariant solutions. This strengthens the main result of (arXiv:2201.03487), and is potentially important for the identification of the limit of other approximations, such as lattice dynamics. Our proof relies on systematic short-time expansions of singular stochastic PDEs and of regularised Wilson loops. We also strengthen the recently introduced state spaces to allow finer control on line integrals appearing in expansions of Wilson loops. Show Chinese abstract

Abstract: 在 (arXiv:2201.03487) 中构造了 3D 随机量子化方程的局部解，并且证明了在光滑正则化的极限下，存在一种规范场的质量重整化，使得解是规范协变的。本文证明了导致规范协变解的质量重整化的唯一性。这一结果加强了 (arXiv:2201.03487) 的主要结论，并且对于识别其他逼近（例如格点动力学）的极限可能具有重要意义。我们的证明依赖于奇异随机偏微分方程和正则化威尔逊圈的系统性短时间展开。我们还加强了最近引入的状态空间，以更好地控制威尔逊圈展开中出现的线积分。