3+2 De Sitter Superfields

Abstract

An efficient treatment of de Sitter supersymmetry makes it possible to present a rather complete group theoretical analysis of de Sitter supeifields. Much of the analysis is independent of the type and number of indices on the superfield. The covariant derivatives form a 5-dimensional representation of osp(4/l). The invariant operator formed from the covariant derivatives (the Dirac operator) provides, by its spectral decomposition, a reduction of the field into irreducible parts (in the massive case). Greatest emphasis is placed on the massless case, and a complete account is presented of the interesting nondecomposable representations that appear. The vector multiplet is described by a superfield analog of the Fierz-Pauli equation. Its massless limit (super QED) is analyzed in detail, with its full gauge structure and indefinite metric quantization. A chirality operator is also described, and a preliminary discussion of N = 2 extended superfields. A strong analogy between N = 2 supersymmetry and conformal invariance is pointed out and related to the difficulties that still confront the completion of N = 2 superspace field theory.