Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups

We show that there is a remarkable connection between the harmonic superspace (HSS) formulation of N=2, d=4 supersymmetric quaternionic Kaehler sigma models that couple to N=2 supergravity and the minimal unitary representations of their isometry groups. In particular, for N=2 sigma models with quaternionic symmetric target spaces of the form G/HXSU(2) we establish a one-to-one mapping between the Killing potentials that generate the isometry group G under Poisson brackets in the HSS formulation and the generators of the minimal unitary representation of G obtained by quantization of its geometric realization as a quasiconformal group. Quasiconformal extensions of U-duality groups of four dimensional N=2, d=4 Maxwell-Einstein supergravity theories (MESGT) had been proposed as spectrum generating symmetry groups earlier. We discuss some of the implications of our results, in particular, for the BPS black hole spectra of 4d, N=2 MESGTs.Comment: 20 pages; Latex file: references added; minor cosmetic change

Unified Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Five Dimensions

Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple Euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (Minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N=2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets.Comment: Latex 2e, 28 pages. v2: reference added, footnote 14 enlarge