Vacuum Energies of Non--Abelian String--Configurations in 3+1 Dimensions

We develop a method to compute the fermion contribution to the vacuum polarization energy of string--like configurations in a non--abelian gauge theory. This calculation has been hampered previously by a number of technical obstacles. We use gauge invariance of the energy and separation of length scales in the energy density to overcome these obstacles. We present a proof-of-principle investigation that shows that this energy is small in the MS-bar renormalization scheme. The generalization to other schemes is straightforward.