Local Supersymmetry in One-Loop Quantum Cosmology

The contribution of physical degrees of freedom to the one-loop amplitudes of Euclidean supergravity is here evaluated in the case of flat Euclidean backgrounds bounded by a three-sphere, recently considered in perturbative quantum cosmology. The physical degrees of freedom (denoted by PDF) are picked out by imposing the supersymmetry constraints and choosing a gauge condition. Remarkably, for the massless gravitino field the PDF method and local boundary conditions lead to a result for the trace anomaly which is equal to the PDF value one obtains using spectral boundary conditions on a 3-sphere.