Stability of magnetic condensation and mass generation for confinement in SU(2) Yang-Mills theory

TL;DR

This paper demonstrates that the Nielsen-Olesen instability in the Savvidy vacuum is absent in SU(2) Yang-Mills theory due to dynamical gluon mass generation, supporting the dual superconductor model of confinement.

Contribution

It shows the stability of the Yang-Mills vacuum with chromomagnetic condensation and links gluon mass generation to confinement mechanisms.

Findings

Nielsen-Olesen instability disappears in SU(2) Yang-Mills.

Dynamical gluon mass arises from a BRST-invariant condensate.

Results support the dual superconductor picture of confinement.

Abstract

In the framework of the functional renormalization group, we reexamine the stability of the Yang-Mills vacuum with a chromomagnetic condensation. We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the $SU(2)$ Yang-Mills theory. As a physical mechanism for maintaining the stability even for the small infrared cutoff, we argue that dynamical gluon mass generation occurs due to a BRST-invariant vacuum condensate of mass dimension-two, which is related to two-gluon bound states identified with glueballs. These results support the dual superconductor picture for quark confinement.