Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups

Abstract

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.

20 pages; Latex file: references added; minor cosmetic changes

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Cited by in corpus (7)

• Freudenthal Duality and Generalized Special Geometry
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
• Minimal unitary representation of D(2,1;λ) and its SU(2) deformations and d=1, N=4 superconformal models
• Quaternion-Kähler N=4 Supersymmetric Mechanics