N=8 non-BPS attractors, fixed scalars and magic supergravities

We analyze the Hessian matrix of the black hole potential of N=8, d=4 supergravity, and determine its rank at non-BPS critical points, relating the resulting spectrum to non-BPS solutions (with non-vanishing central charge) of N=2, d=4 magic supergravities and their “mirror” duals. We find agreement with the known degeneracy splitting of N=2 non-BPS spectrum of generic special Kähler geometries with cubic holomorphic prepotential. We also relate non-BPS critical points with vanishing central charge in N=2 magic supergravities to a particular reduction of the N=8, 18-BPS critical points.