In the presence of a string, we calculate the index of the Dirac operator for 2n chiral fermions which get their masses through couplings to various scalar fields with arbitrary phase variations around the string. This calculation generalizes known results and is, in many cases of cosmic strings in realistic models, the only available information for the existence of fermionic zero modes, necessary for string superconductivity.

• Received 14 December 1987

DOI:https://doi.org/10.1103/PhysRevD.38.547