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

We correct two errors in our previous computation of one-loop corrections to the vortex string tension: (i) the contribution of the longitudinal and timelike modes of the gauge fields were forgotten and are included now; (ii) a trivial error in the numerical code has led to considerable errors in the subtracted integrals. We here present the corrected results.