  We calculate the one loop gluon vacuum energy in the background of a color
magnetic vortex for SU(2) and SU(3). We use zeta functional regularization to
obtain analytic expressions suitable for numerical treatment. The momentum
integration is turned to the imaginary axis and fast converging sums/integrals
are obtained. We investigate numerically a number of profiles of the
background. In each case the vacuum energy turns out to be positive increasing
in this way the complete energy and making the vortex configuration less
stable. In this problem bound states (tachyonic modes) are present for all
investigated profiles making them intrinsically unstable.
