Large dual transformations and the Petrov-Diakonov representation of the Wilson loop

Abstract

In this work, based on the Petrov-Diakonov representation of the Wilson loop average $\overline{W}$ 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 $\overline{W}$ 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.