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تسجيل مستخدم جديدAttractors with Vanishing Central Charge
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We consider the Attractor Equations of particular $mathcal{N}=2$, d=4 supergravity models whose vector multiplets scalar manifold is endowed with homogeneous symmetric cubic special K{a}hler 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 $mathcal{N}=2$ central charge. Such formulae hold 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 $mathcal{N}=8$, d=4 supergravity, we give an interpretation of such a relation as an exchange of two of the four eigenvalues of the $mathcal{N}=8$ central charge matrix $Z_{AB}$. We also consider non-BPS attractors with non-vanishing $mathcal{Z}$; for peculiar charge configurations, we derive solutions violating the Ansatz usually formulated in literature. Finally, by group-theoretical considerations we relate Cayleys hyperdeterminant (the invariant of the stu model) to the invariants of the st^{2} and of the so-called t^{3} model.
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