Cosmic string zero modes and multiple phase transitions

The zero modes and current carrying capability of a cosmic string formed at one phase transition can be modified at subsequent phase transitions. A new, generalised index theorem is derived that is applicable to theories with multiple phase transitions. This enables us to investigate the fate of string zero modes during sequences of phase transitions in a variety of models. Depending on the couplings that the breaking introduces, the zero modes may be destroyed and the superconductivity of the string removed, and thus vortons dissipate. We discuss the features of the theory that are required to produce this behaviour and consider the implications of spectral flow.