We study both the large and small U-duality charge orbits of extremal black holes appearing in $D=5$ and $D=4$ Maxwell-Einstein supergravity theories with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan algebras and their associated Freudenthal triple systems, in order to derive the minimal charge representatives, their stabilizers and the associated “moduli spaces.” After recalling $\mathcal{N}=8$ maximal supergravity, we consider $\mathcal{N}=2$ and $\mathcal{N}=4$ theories coupled to an arbitrary number of vector multiplets, as well as $\mathcal{N}=2$ magic, $STU$, $S{T}^2$ and $T^3$ models. While the $STU$ model may be considered as part of the general $\mathcal{N}=2$ sequence, albeit with an additional triality symmetry, the $S{T}^2$ and $T^3$ models demand a separate treatment, since their representative Jordan algebras are Euclidean or only admit nonzero elements of rank 3, respectively. Finally, we also consider minimally coupled $\mathcal{N}=2$, matter-coupled $\mathcal{N}=3$, and pure $\mathcal{N}=5$ theories.

• Received 30 October 2011

DOI:https://doi.org/10.1103/PhysRevD.85.086002