Gravitino Zero Modes on U(1)_R Strings

We consider theories with a spontaneously broken gauged R-symmetry, which can only occur in supergravity models. These give rise to cosmic R-strings upon which gravitino zero modes can exist. We construct solutions to the Rarita-Schwinger spin-3/2 equation describing the gravitino in the field of these cosmic strings and show that under some conditions these solutions may give rise to gravitino currents on the string. We discuss further mathematical and physical questions associated with these solutions.