Small black hole constituents and horizontal symmetry

By exploiting the role of the horizontal symmetry \( S{L_h}\left( {2,\mathbb{R}} \right) \), we extend the analysis and classification of two-centered extremal black hole charge configurations to the case of “small” single-centered constituents. These latter are seen to decrease the number of independent horizontal-invariant polynomials from four to one, depending on the rank of the charge orbit supporting each of the two centers. Within U-duality groups of type E 7, both reducible and irreducible symmetric supergravity models in four space-time dimensions are considered, thus encompassing \( \mathcal{N} = 2 \) and \( \mathcal{N} = 8 \) theories.