  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.
