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Attractors with vanishing central charge

Profile image of Alessio MarraniAlessio Marrani

2007, Physics Letters B

https://doi.org/10.1016/J.PHYSLETB.2007.08.079
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18 pages

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Abstract

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 Kähler 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 formulae 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 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. * On leave of absence from JINR, Dubna, Russia In the framework of N = 2, d = 4 supergravity, such an horizon geometry is associated to the maximal N = 2 supersymmetry algebra psu(1, 1 |2), which is an interesting example of superalgebra containing not Poincaré nor semisimple groups, but direct products of simple groups as maximal bosonic subalgebra. Indeed, in this case the maximal bosonic subalgebra is so(1, 2) ⊕ su(2) (with related maximal spin bosonic subalgebra su(1, 1) ⊕ su(2)), matching the corresponding bosonic isometry group of the Bertotti-Robinson metric (1.1).

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