Spin-3/2 Potentials in Backgrounds with Boundary

TL;DR

This paper investigates the boundary conditions and gauge invariances of massless Rarita-Schwinger fields in four-dimensional Riemannian backgrounds, concluding that only totally flat geometries are compatible with the boundary conditions and gauge transformations.

Contribution

It demonstrates that in the massless case, the Rarita-Schwinger potentials and secondary potentials restrict the background to be totally flat, clarifying gauge invariance constraints with boundaries.

Findings

Only totally flat backgrounds are compatible with boundary conditions.

Gauge transformations restrict the gauge freedom in the presence of boundaries.

Secondary potentials further restrict the background geometry to be flat.

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.