Stability of chromomagnetic 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 resolved within the functional renormalization group framework, supporting stable chromomagnetic condensation and gluon mass generation in SU(2) Yang-Mills theory.

Contribution

It shows the disappearance of the Nielsen-Olesen instability using the functional renormalization group, indicating stable chromomagnetic condensation and gluon mass generation without instability.

Findings

Vanishing imaginary part of the effective average action at fixed points.

Analytical solutions without imaginary parts for large infrared cutoff.

Evidence for dynamical gluon mass generation from vacuum condensates.

Abstract

We show that the Nielsen-Olesen instability of the Savvidy vacuum with a homogeneous chromomagnetic condensation disappears in the framework of the functional renormalization group. This result follows from our observations: (i) the vanishing imaginary part of the effective average action is realized for arbitrary infrared cutoff as a novel fixed point solution of the flow equation for the complex-valued effective average action and (ii) an approximate analytical solution for the effective average action is obtained without the pure imaginary part for large infrared cutoff. This result suggests that there exists a physical mechanism for maintaining the stability or staying on the fixed point even for sufficiently small infrared cutoff. We argue that dynamical gluon mass generation (related to two-gluon bound states identified with glueballs) occurs due to the Becchi-Rouet-Stora-Tyutin-invariant vacuum condensate of mass dimension two without causing instability.