Large Dual Transformations and the Petrov-Diakonov Representation of the Wilson Loop

TL;DR

This paper explores the Petrov-Diakonov representation of the Wilson loop in SU(2) Yang-Mills theory, providing a framework to understand confinement and defect ensembles through dual transformations and surface decoupling.

Contribution

It introduces a natural framework combining the Petrov-Diakonov representation with the Cho-Fadeev-Niemi decomposition to analyze the role of surfaces and dual fields in confinement mechanisms.

Findings

Surface decoupling depends on ensemble regularity properties.

Large dual transformations can be enabled or disabled by the ensemble choice.

The framework links defect ensembles to the behavior of the Wilson loop surface.

Abstract

In this work, based on the Petrov-Diakonov representation of the Wilson loop average W in the SU(2) Yang-Mills theory, together with the Cho-Fadeev-Niemi decomposition, we present a natural framework to discuss possible ideas underlying confinement and ensembles of defects in the continuum. In this language we show how for different ensembles the surface appearing in the Wess-Zumino term in W can be either decoupled or turned into a variable, to be summed together with gauge fields, defects and dual fields. This is discussed in terms of the regularity properties imposed by the ensembles on the dual fields, thus precluding or enabling the possibility of performing the large dual transformations that would be necessary to decouple the initial surface.