Jordan meets Freudenthal. A black hole exceptional story

Abstract

Within the extremal black hole attractors arising in ungauged \mathcal{N}≥2𝒩≥2-extended Maxwell Einstein supergravity theories in 3+13+1 space-time dimensions, we provide an overview of the stratification of the electric-magnetic charge representation space into “large” orbits and related “moduli spaces”, under the action of the (continuous limit of the) non-compact UU-duality Lie group. While each “large” orbit of the UU-duality supports a class of attractors, the corresponding ” moduli space” is the proper subspace of the scalar manifold spanned by those scalar fields on which the Attractor Mechanism is inactive. We present the case study concerning \mathcal{N}=2𝒩=2 supergravity theories with symmetric vector multiplets’ scalar manifold, which in all cases (with the exception of the minimally coupled models) have the electric-magnetic charge representation of UU-duality fitting into a reduced Freudenthal triple system over a cubic (simple or semi-simple) Jordan algebra.