Expansion in the width: the case of vortices Original Research Article

We construct an approximate solution of field equations in the Abelian Higgs model which describes motion of a curved vortex. The solution is found to the first order in the inverse mass of the Higgs field with the help of the Hilbert-Chapman-Enskog method. Consistency conditions for the approximate solution are obtained with the help of a classical Ward identity. We find that the Higgs field of the curved vortex of the topological charge n ≥ 2 in general does not have single n-th order zero. There are two zeros: one is of the (n − 1)-th order and it follows a Nambu-Goto type trajectory, the other one is of the first order and its trajectory in general is not of the Nambu-Goto type. For |n| = 1 the single zero in genera] does not lie on Nambu-Goto type trajectory.