# Yang-Mills for probabilists

## TL;DR

This paper discusses the formulation of Euclidean Yang-Mills theories as problems in probability theory, aiming to contribute to the rigorous construction of quantum Yang-Mills theories in four dimensions.

## Contribution

It presents a probabilistic formulation of core aspects of Euclidean Yang-Mills theories and lattice gauge theories, highlighting key open problems and their mathematical context.

## Key findings

- Identifies core problems in probability related to Euclidean Yang-Mills theories.
- Connects lattice gauge theories with continuum limits in a probabilistic framework.
- Reviews existing mathematical literature on the topic.

## Abstract

The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This article presents a formulation of some of the core aspects this problem as problems in probability theory. The presentation begins with an introduction to the basic setup of Euclidean Yang-Mills theories and lattice gauge theories. This is followed by a discussion of what is meant by a continuum limit of lattice gauge theories from the point of view of theoretical physicists. Some of the main issues are then posed as problems in probability. The article ends with a brief review of the mathematical literature.