QCD effective action and stability of magnetic condensation

Abstract

We present two independent arguments to resolve the controversy on the stability of the magnetic condensation in QCD. We calculate the imaginary part of the one-loop effective action of SU(2) QCD in two different methods, and show that the gauge invariant calculation of the functional determinant assures the stability of the magnetic condensation. We confirm the stability calculating the imaginary part of the effective action perturbatively, with Fyenman diagram and Schwinger's method. We generalise this result to SU(3) QCD and show that, in the presence of chromomagnetic background, the real part of the effective action has true minimum only when (H) over right arrow (3) and (H) over right arrow (8) becomes orthogonal. Moreover, with the chromomagnetic background the effective action has no imaginary part, but with the chromoelectric background it acquires a negative imaginary part. This strongly indicates the existence of a stable monopole condensation in QCD.