Geometrical first order supergravity in five space time dimensions

In this paper we present the first order formulation of five-dimensional supergravity. According to the group manifold approach discussed in previous papers we introduce a potential field 1-form in the adjoint representation of the S-barU-bar(2,2/1)Lie algebra (the minimal grading of five-dimensional Poincare algebra). Imposing Lorentz gauge invariance and the existence of nontrivial solutions besides the vacuum, the Lagrangian is then constructed without use of the Hodge duality operator (Maxwell-type kinetic terms). It turns out that two different theories exist in the first order formulation, both SO(1,4)xU(1) gauge invariant and supersymmetric. Going to the second order formalism the two theories become identical and the spin 1 kinetic term is generated. The dichotomy present in the first order version of the theory may be of some importance for quantization. The introduction of a cosmological constant and the reintroduction of the noncontracted group SU(2,2/1) is trivial in this approach as in N = 1 supergravity. At the end of the paper we explicity exhibit the de Sitter version of the theory. It must be noted that this is the second example of completely pure geometrical supersymmetric theory known to date. By pure we mean that no other field except the Lie Algebra valued 1-form potential is needed