On the Vacuum energy of a Color Magnetic Vortex

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.