Attractors with vanishing central charge

We consider the attractor equations of particular N = 2, d = 4 supergravity models whose vector multiplets' scalar manifold is endowed with homogeneous symmetric cubic special Kahler geometry, namely of the so-called st(2) and stu models. In this framework, we derive explicit expressions for the critical moduli corresponding to non-BPS attractors with vanishing N = 2 central charge. Such formul ae hold for a generic black hole charge configuration, and they are obtained without formulating any ad hoc simplifying assumption. We find that such attractors are related to the 1/2-BPS ones by complex conjugation of some moduli. By uplifting to N = 8, d = 4 supergravity, we give an interpretation of such 2 a relation as an exchange of two of the four eigenvalues of the N = 8 central charge matrix Z(AB). We also consider non-BPS attractors with non-vanishing Z; for peculiar charge configurations, we derive solutions violating the ansatz usually formulated in literature. Finally, by group-theoretical considerations we relate Cayley's hyperdeterminant (the invariant of the stu model) to the invariants of the st(2) and of the so-called t(3) model. (C) 2007 Elsevier B.V. All rights reserved.