Two-centered magical charge orbits

We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2, R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product < Q(1), Q(2)>, known to control the mutual non-locality of the two centers.