ONE-LOOP DIVERGENCES IN SIMPLE SUPERGRAVITY - BOUNDARY EFFECTS

This paper studies the semiclassical approximation of simple supergrav ity in Riemannian four-manifolds with a boundary, within the framework of zeta-function regularization. The massless nature of gravitinos, j ointly with the presence of a boundary and a local description in term s of potentials for spin 3/2, force the background to be totally flat. First, nonlocal boundary conditions of the spectral type are imposed on spin-3/2 potentials, jointly with boundary conditions on metric per turbations which are completely invariant under infinitesimal diffeomo rphisms. The axial gauge-averaging functional is used, which is then s ufficient to ensure self-adjointness. One, thus, finds that the contri butions of ghost and gauge modes vanish separately. Hence the contribu tions to the one-loop wave function of the universe reduce to those ze ta(0) values resulting from physical modes only. Another set of mixed boundary conditions, motivated instead by local supersymmetry and firs t proposed by Luckock, Moss, and Poletti, is also analyzed. In this ca se the contributions of gauge and ghost modes do not cancel each other . Both sets of boundary conditions lead to a nonvanishing zeta(0) valu e, and spectral boundary conditions are also studied when two concentr ic three-sphere boundaries occur. These results seem to point out that simple supergravity is not even one-loop finite in the presence of bo undaries.