Diagonal deformations of thin center vortices and their stability in Yang-Mills theories

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 thick center vortex backgrounds. They display the so called Savvidy-Nielsen-Olesen instability, associated with a gyromagnetic ratio g(m)((b)) = 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 in SU(N) Yang-Mills theories. Then, we define a thick object as a diagonal deformation of the thin center vortex. Besides the usual thick background profile, this deformation also contains a frame defect coupled with gyromagnetic ratio g(m)((d)) = 1. As a consequence, the analysis of stability is modified. In particular, we point out that the defect should stabilize a vortex configuration formed by a pair of straight components with opposite fluxes, separated by an appropriate finite distance.