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Jordan meets Freudenthal. A black hole exceptional story

Alessio Marrani

SciPost Phys. Proc. 14, 009 (2023) · published 23 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


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.

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