Fermionic zero modes for cosmic strings

In the presence of a cosmic string, we determine separately the number of right- and left-moving transverse zero modes of the Dirac equation for 2n chiral fermions which get their masses through couplings to various scalar fields with arbitrary phase variations around the string. This result provides us with an unambiguous criterion for string superconductivity in 'realistic' grand unified and superstring inspired models. As an application, we determine the zero modes of a superheavy L-R string of a specific superstring inspired model. We find that this string is superconducting, through fermionic charge carriers, provided that electric charge and colour is conserved on the string core. (orig.)