LINE VORTICES IN HIGGS ABELIAN MODEL

Let x(1), x(2),..., x(n) be n distinct points of R(3) and E be a U(1)- fibre bundle of basis R(3)\{x(1), x(2),..., x(n)}, we prove the existe nce of minimizers for the Higgs functional and we study their behaviou r when the coupling constant tends to infinity. We prove, in particula r, that the lack of compactness concentrates along lines which connect the monopoles x(i) a number of time given by the topology of E around the x(i). This work is the three-dimensional equivalent of [3] and [1 ].