Resolving the instability of the Savvidy vacuum by dynamical gluon mass

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>.