Resolving the instability of the Savvidy vacuum by dynamical gluon mass

TL;DR

This paper demonstrates that incorporating a dynamical gluon mass resolves the Savvidy vacuum instability, showing that the vacuum prefers a nonzero gluon condensate with negligible chromomagnetic field, eliminating the Nielsen-Olesen instability.

Contribution

It introduces a formalism combining local composite operators with chromomagnetic fields to resolve the Savvidy vacuum instability through dynamical gluon mass effects.

Findings

Vacuum energy minimized by nonzero <A_2> condensate

Chromomagnetic field near zero in the stable vacuum

Nielsen-Olesen instability is eliminated

Abstract

In this paper we apply the formalism of local composite operators as developed by Verschelde et al. in combination with a constant chromomagnetic field as considered in the seventies by Savvidy and others. We find that a nonzero <A_\mu^2> minimizes the vacuum energy, as in the case with no chromomagnetic field, and that the chromomagnetic field itself is near-to zero. The Nielsen-Olesen instability, caused by the imaginary part in the action, also vanishes. We further investigate the effect of an external chromomagnetic field on the value of <A_\mu^2>, finding that this condensate is destroyed by sufficiently strong fields. The inverse scenario, where <A_\mu^2> is considered as external, results in analogous findings: when this condensate is sufficiently large, the induced chromomagnetic field is lowered to a perturbative value slightly below the applied <A_\mu^2>.