SPIN-$\frac{3}{2}$ POTENTIALS IN BACKGROUNDS WITH BOUNDARY

Abstract

This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat. The analysis of other gauge transformations confirms that, in the massless case, the only admissible class of Riemannian backgrounds with boundary is totally flat.