Non - Local Boundary Conditions for Massless Spin - 12 Fields

This paper studies the 1-loop approximation for a massless spin-1/2 field on a flat four-dimensional Euclidean background bounded by two concentric 3-spheres, when non-local boundary conditions of the spectral type are imposed. The use of ζ-function regularization shows that the conformal anomaly vanishes, as in the case when the same field is subject to local boundary conditions involving projectors. A similar analysis of nonlocal boundary conditions can be performed for massless supergravity models on manifolds with boundary, to study their 1-loop properties.