One-loop corrections to the string tension of the vortex in the Abelian Higgs model

We present an exact numerical computation of the one-loop correction of the string tension for the Nielsen-Olesen vortex in the Abelian Higgs model. The computation proceeds via the computation of the Euclidean Green's function for the gauge, Higgs, and Faddeev-Popov fields using mode functions, and taking the appropriate trace. Renormalization is an essential part of this computation. It is done by removing leading order contributions from the numerical results so as to make these finite, and to add the divergent parts back, after suitable regularization and renormalization. We encounter and solve some problems which are specific to gauge theories and topological solutions. The corrections to the energy are found to be sizable, but still smaller than the classical energy as long as g(2) is smaller than unity.