Attractors with Vanishing Central Charge
arXiv:0707.2730 · doi:10.1016/j.physletb.2007.08.079
Abstract
We consider the Attractor Equations of particular , d=4 supergravity models whose vector multiplets' scalar manifold is endowed with homogeneous symmetric cubic special Kähler geometry, namely of the so-called and models. In this framework, we derive explicit expressions for the critical moduli corresponding to non-BPS attractors with vanishing central charge. Such formulæhold for a generic black hole charge configuration, and they are obtained without formulating any \textit{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 , d=4 supergravity, we give an interpretation of such a relation as an exchange of two of the four eigenvalues of the central charge matrix . We also consider non-BPS attractors with non-vanishing ; 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.
17 pages, LaTeX file
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