Monopole Condensation and Dimensional Transmutation in SU(2) QCD

TL;DR

This paper confirms monopole condensation stability in SU(2) QCD by calculating the effective action's imaginary part, showing magnetic backgrounds are stable while electric backgrounds are unstable due to gluon pair-annihilation.

Contribution

It resolves a controversy by demonstrating monopole condensation stability through two different one-loop effective action calculations in SU(2) QCD.

Findings

Magnetic background effective action has no imaginary part.

Electric background effective action has a negative imaginary part.

Monopole condensation is stable, electric background is unstable.

Abstract

We resolve the controversy on the stability of the monopole condensation in the one-loop effective action of SU(2) QCD by calculating the imaginary part of the effective action with two different methods at one-loop order. Our result confirms that the effective action for the magnetic background has no imaginary part but the one for the electric background has a negative imaginary part. This assures that the monopole condensation is indeed stable, but the electric background becomes unstable due to the pair-annihilation of gluons.