Bound States and Instabilities of Vortices

We examine the spectrum of small perturbations around global and local (gauge) abelian vortices, using simple numerical matrix techniques. The results are of interest for both cosmic strings and for their condensed matter analogues, superfluid and superconducting vortices. We tabulate the instabilities of higher winding number vortices, and find several bound states. These localised oscillations of the order parameter can be thought of as particle states trapped in the core of the string.