Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups

TL;DR

This paper reveals a deep connection between harmonic superspace formulations of N=2 supersymmetric models and the minimal unitary representations of their isometry groups, with implications for black hole spectra.

Contribution

It establishes a one-to-one correspondence between Killing potentials in harmonic superspace and minimal unitary group representations for quaternionic symmetric spaces.

Findings

Mapping between Killing potentials and minimal unitary representations.

Implications for BPS black hole spectra in N=2 supergravity.

Extension of U-duality groups as spectrum generators.

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.