An almost simple off-shell version of SU(2) Poincaré supergravity

Abstract

We present a new version of N = 2 Poincaré supergravity which is algebraically simple. We include the “non-trivial” SU(2) in the gauge group and can then impose constraints on the geometry of superspace such that all low-dimensional components of torsion and curvatures are constant. Then only a moderate number of non-linear terms appear in the supersymmetry transformation laws. This simplification makes it feasible to explicitly calculate the lagrangian for the gauge field multiplets of Yang-Mills symmetry groups and of the “non-trivial” SU(2). Propagating SU(2) gauge fields give rise to a cosmological constant and to spontaneous breaking of the supersymmetries and of the SU(2).