NONCOMPACT N=2 SUPERGRAVITY

A massive spin-one multlplet with central charge IS coupled to N=2 supergravity. Compared to conventional gauge fields the anomalous magnetic moment of the spin-one particles is of the opposite sign. The construction of this theory is based on an N=2 supersymmetric gauge theory associated with the noncompact group SO(2,1). As a byproduct we present aconve-nient expression for the N=2 Emstein-Yang-Mills agrangian. As is well-known, noncompact symmetry groups have quadratic invariants that are not positive definite. This aspect limits their applicability in realistic field theories, where one must insist on states with positive norm. The standard solution to this problem is to ensure that the noncompact transformations are realized nonlinearly. This can be achieved by introducing a nonlinear sigma model in which the fields parametrize the coset space G/H, where H is the maximal compact subgroup of the noncompact group G [ 1]. All other fields are assigned to representations of H and not of G. The compact group H acts then linearly on all the fields, whereas the noncompact transforma-tions act nonlinearly. These nonlinear transformations take the form of an H transformation, but with parameters that depend on the fields of the nonlinear sigma model. It is possible to formulate this theory in such a way that the full group G is realized linearly on the fields. In that case the group H is promoted to an independent local gauge group, so that the lagrangian is manifestly invari-ant under Gngid × Hloca 1. Because G is noncompact the kinetic term for the scalars contains fields whose contribu