Reconstructing the Vacuum Functional of Yang-Mills from its Large Distance Behaviour

TL;DR

This paper develops a method to reconstruct the vacuum functional of Yang-Mills theory for arbitrary fields by re-summing an expansion valid for slowly varying fields, connecting large-distance behavior to the full functional.

Contribution

It introduces a novel approach to re-sum the local functional expansion of the vacuum functional, enabling analysis beyond slowly varying fields in Yang-Mills theory.

Findings

Re-summation technique for the vacuum functional

Connection between large-distance behavior and full functional

Reconstruction of the vacuum functional for arbitrary fields

Abstract

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals. For Yang-Mills theory the leading term in the expansion dominates large distance effects and leads to an area law for the Wilson loop. However, this expansion cannot be expected to converge for fields that vary more rapidly. By studying the analyticity of the vacuum functional under scale transformations we show how to re-sum this series so as to reconstruct the vacuum functional for arbitrary fields.