Diagonal deformations of thin center vortices and their stability in Yang-Mills theories
Abstract
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 g(b)m=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 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 g(d)m=1, originated from the charged sector. 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 separated by an appropriate finite distance.