a family of classically degenerate BPS kinks repulsive forces were induced by the quantum fluctuations that broke the classical degeneracy. We plan to address an identical issue in the moduli space of BPS vortices in the Abelian Higgs model. Jaffe and Taubes showed in [@Jaffe1980] that the vortex moduli space is the set of $N$ unordered points in $\mathbb{R}^2$. As a consequence vortices with one quantum of magnetic flux move freely without any interaction. The $2N$ vortex zero modes obey to this freedom in the critical point between Type II and Type I superconductivity phases, in the first case surge repulsive whereas in the second case attractive forces between vortices. We shall discuss wether or not this classical picture is maintained at one-loop order after the effect of vortex fluctuations is accounted for. We shall perform the pertinent calculations generalizing the improved GdW heat kernel procedure developed previously for scalar field theories to Abelian gauge theories with spontaneous symmetry breaking. The analysis will be first focused in the planar AHM where the BPS vortices are topological solitons. After that we shall move to study the same problem in a three dimensional space, where we find BPS vortices magnetic tubes or 