### On the Vacuum Energy of the Color Magnetic Vortex

**M. Bordag**

*Institute for Theoretical Physics*

University of Leipzig

Augustusplatz 10

04109 Leipzig, Germany

We calculate the 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 order to find out which
configuration minimizes the total energy of the system. In this
problem bound states (tachyonic modes) turn out to be present
for all investigated profiles making them intrinsically unstable.