标题： 曲线上的亚纯联络的重正则描述 显示英文标题

标题： A renormalised description of meromorphic connections over curves

摘要： 重整化群（RG）是一种系统的方法，用于正规化在构造一大类微分问题解时出现的发散现象，这些发散现象是作为人工效应出现的，无论是微扰还是非微扰情况下。 本文致力于在复流形上全纯主丛的可去连接的平坦截面的非微扰背景下进行这种操作，其李群具有半单和复结构。 利用Kunuhiro对RG在解族包络线意义上的解释，我们将这些包络线识别为与相应量子谱曲线上的点相关的特定平坦截面，即基曲线上带有伴随丛中局部系数的某些除子，从而得到积分表示。 这表明，在通过其量子几何或同调描述可去连接时，曲线上的主丛平坦截面的非微扰重整化自然地融入其中，\textit{按 la}Goldman，其中平坦截面及其变形分别由零次和一次链参数化。 最后，我们提及即将到来的应用。 显示英文摘要

摘要： The Renormalisation Group (RG) is a systematic procedure used to regularise divergences appearing as artefacts when constructing solutions to a large class of differential problems, whether perturbatively or not. This paper is devoted to performing it in the non-perturbative context of flat sections of meromorphic connections in holomorphic principal bundles over a base complex curve, with reductive and complex structure Lie groups. Using the interpretation of Kunuhiro of RG in terms of envelopes of families of solutions, we identify these envelopes as particular flat sections associated to points on the corresponding quantum spectral curve, namely certain divisors on the base curve with local coefficients in the adjoint bundle, yielding integral representations. This shows that the non-perturbative renormalisation of flat sections of principal bundles over curves fits naturally within the description of meromorphic connections via their quantum geometry, or homology \textit{\`a la} Goldman, where the flat sections and their deformations are parameterized by degree zero and one chains respectively. We conclude the paper by mentioning upcoming applications.