# Geometrical first order supergravity in five space time dimensions

- Authors
- Journal
- Annals of Physics 0003-4916
- Publisher
- Elsevier
- Publication Date
- Volume
- 135
- Issue
- 2
- Identifiers
- DOI: 10.1016/0003-4916(81)90155-x
- Disciplines

## Abstract

Abstract 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 SU(2, 2 1 ) Lie algebra (the minimal grading of five-dimensional Poincaré 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) ⊗ U(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 explicitly exhibit the de Sitter version of the theory. It must be noted that this is the second example of a 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.

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