Monopole condensation and dimensional transmutation in SU(2) QCD

We resolve the controversy regarding 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 confirms that the monopole condensation is indeed stable, but the electric background becomes unstable due to the pair-annihilation of gluons.