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

TL;DR

This paper investigates the stability of center vortices in SU(N) Yang-Mills theories, proposing a diagonal deformation approach that introduces a defect stabilizing vortex configurations, addressing continuum relevance concerns.

Contribution

It introduces a new diagonal deformation of thin center vortices with a defect that potentially stabilizes vortex configurations in continuum Yang-Mills theories.

Findings

Defect stabilizes vortex pairs separated by finite distance

Deformation modifies the stability analysis of vortices

Addresses continuum relevance of center vortices

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 {\it 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.