Large deviations for the Yang-Mills measure on a compact surface

TL;DR

This paper establishes a large deviation principle for the Yang-Mills measure on a compact surface, linking it rigorously to the Yang-Mills energy at small volume limits, providing a foundational mathematical result.

Contribution

It is the first to mathematically connect the Yang-Mills measure with the Yang-Mills energy via large deviations on a compact surface.

Findings

Yang-Mills measures satisfy a large deviation principle at small volume limits.

The rate function is expressed in terms of the Yang-Mills energy.

This result provides a new rigorous understanding of the measure-energy relationship.

Abstract

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energy.