Gauge invariance and vacuum energies of non-Abelian string-configurations

We improve on a method to compute the fermion contribution to the vacuum polarization energy of string-like configurations in a non-Abelian gauge theory. We establish the new method by numerically verifying the invariance under (a subset of) local gauge transformations. This also provides further support for the use of spectral methods to compute vacuum polarization energies in general. We confirm that the vacuum energy in the MS¯ renormalization scheme is tiny as compared to the mass of the fluctuating fermion field. Numerical results for the physical on-shell scheme are also presented.