Abstract
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 , 1 8 -BPS critical points.
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