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 both for cosmic strings and for their condensed matter analogues, superfluid and superconductor vortices. We tabulate the instabilities of higher winding number vortices, and find several bound states. These localised coherent oscillations of the order parameter can be thought of as particle states trapped in the core of the string. e-mail: [email protected] e-mail: [email protected]