A State Space for 3D Euclidean Yang-Mills Theories

被引：2

作者：

Cao, Sky ^{[1
]}

Chatterjee, Sourav ^{[2
]}

机构：

[1] MIT, Dept Math, Bldg 2, Cambridge, MA 02138 USA

[2] Stanford Univ, Dept Stat, Sequoia Hall,390 Jane Stanford Way, Stanford, CA 94305 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2024年 / 405卷 / 01期

关键词：

QUANTIZED GAUGE-FIELDS; CONSTRUCTION; CONVERGENCE; CONNECTIONS;

D O I：

10.1007/s00220-023-04870-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is believed that Euclidean Yang-Mills theories behave like the massless Gaussian free field (GFF) at short distances. This makes it impossible to define the main observables for these theories-the Wilson loop observables-in dimensions greater than two, because line integrals of the GFF do not exist in such dimensions. Taking forward a proposal of Charalambous and Gross, this article shows that it is possible to define Euclidean Yang-Mills theories on the 3D unit torus as 'random distributional gauge orbits', provided that they indeed behave like the GFF in a certain sense. One of the main technical tools is the existence of the Yang-Mills heat flow on the 3D torus starting from GFF-like initial data, which is established in a companion paper. A key consequence of this construction is that under the GFF assumption, one can define a notion of 'regularized Wilson loop observables' for Euclidean Yang-Mills theories on the 3D unit torus.

引用

页数：69

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