Magic Supergravities, N= 8 and Black Hole Composites
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We present explicit U-duality invariants for the R, C, Q, O$ (real, complex, quaternionic and octonionic) magic supergravities in four and five dimensions using complex forms with a reality condition. From these invariants we derive an explicit entropy function and corresponding stabilization equations which we use to exhibit stationary multi-center 1/2 BPS solutions of these N=2 d=4 theories, starting with the octonionic one with E_{7(-25)} duality symmetry. We generalize to stationary 1/8 BPS multicenter solutions of N=8, d=4 supergravity, using the consistent truncation to the quaternionic magic N=2 supergravity. We present a general solution of non-BPS attractor equations of the STU truncation of magic models. We finish with a discussion of the BPS-non-BPS relations and attractors in N=2 versus N= 5, 6, 8.
33 pages, references added plus brief outline at end of introduction
33 pages, references added plus brief outline at end of introduction