Jordan meets Freudenthal. A Black Hole Exceptional Story

Abstract

Within the extremal black hole attractors arising in ungauged $\mathcal{N}⩾2$-extended Maxwell Einstein supergravity theories in $3+1$ 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 $U$-duality Lie group. While each "large" orbit of the $U$-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 $\mathcal{N}=2$ 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 $U$-duality fitting into a reduced Freudenthal triple system over a cubic (simple or semi-simple) Jordan algebra.

12 pages, 4 tables. Plenary talk presented at the 34th International Colloquium on Group Theoretical Methods in Physics, Strasbourg, July 18-22, 2022

References in corpus (7)

• Charge Orbits of Symmetric Special Geometries and Attractors
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• N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
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Cited by in corpus (1)

• A coadjoint orbit-like construction for Jordan superalgebras