Small orbits

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 N = 8 maximal supergravity, we consider N = 2 and N = 4 theories coupled to an arbitrary number of vector multiplets, as well as N = 2 magic, STU, ST2 and T-3 models. While the STU model may be considered as part of the general N = 2 sequence, albeit with an additional triality symmetry, the ST2 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 N = 2, matter-coupled N = 3, and pure N = 5 theories.