Gravitino in six-dimensional warped supergravity

We consider the gravitino spectrum for the general warped solution in a specific six-dimensional gauged supergravity. We find that although the brane tensions introduced at the conical singularities break the bulk supersymmetry explicitly, massless modes of the gravitino can exist with a nontrivial wave function profile, due to a nonzero U(1)R gauge flux. We also compute the wave function and the mass spectrum of Kaluza-Klein massive modes of the gravitino explicitly. We show that the introduction of a gravitino mass term on a regularized brane can give a suppressed effective gravitino mass compared to the compactification scale, due to the delocalization of the wave function of the zero-mode gravitino.