Axial Gauge in Quantum Supergravity

This paper studies the role of the axial gauge in the semiclassical analysis of simple supergravity about the Euclidean four-ball, when non-local boundary conditions of the spectral type are imposed on gravitino perturbations at the bounding three-sphere. Metric perturbations are instead subject to boundary conditions completely invariant under infinitesimal diffeomorphisms. It is shown that the axial gauge leads to a non-trivial cancellation of ghost-modes contributions to the one-loop divergence. The analysis, which is based on zeta-function regularization, provides a full $\zeta(0)$ value which coincides with the one obtained from transverse-traceless perturbations for gravitons and gravitinos. The resulting one-loop divergence does not vanish. This property seems to imply that simple supergravity is not even one-loop finite in the presence of boundaries.