Magnetic defects and Wilson surfaces in Yang-Mills theories: observability vs. unobservability

Full text: The importance of center vortices for the understanding of the confining properties of SU(N) Yang-Mills theories is well established in the lattice. However, in the continuum, there is a problem concerning the relevance of center vortex backgrounds. They display the so called Savvidy-Nielsen-Olesen instability, associated with a gyromagnetic ratio gm = 2 for the off-diagonal gluons. In this work, we initially consider the usual definition of a thin center vortex and rewrite it in terms of a local color frame. Then, we define a thick center vortex as a diagonal deformation of the thin object. Besides the usual thick background profile, this deformation also contains a frame defect coupled with gyromagnetic ratio gm = 1, originated from the charged sector. As a consequence of the boundary conditions at the defect, the analysis of stability is modified suggesting that these objects could represent relevant degrees of freedom in continuum Yang-Mills theories. Then, based on the Petrov-Diakonov representation of the Wilson loop, we present a natural framework to discuss possible ideas underlying confinement and ensembles of correlated instantons and thick center vortices. In particular, we show how for different ensembles the surface appearing in the associated Wess-Zumino term ('Wilson surface') can be either decoupled or turned into a variable, to be summed together with defects, gauge 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 Wilson surface. (author)