On some properties of the Attractor Equations

Details On some properties of the Attractor Equations On some properties of the Attractor Equations

2006-02-16

arxiv.org/abs/hep-th/0602161v2

Phys.Lett.B635:172-179,2006

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, to be published in Phys. Lett. B; a misprint in Ref. [13] has been corrected

Scientific paper

10.1016/j.physletb.2006.02.053

We discuss the Attractor Equations of N=2, $d=4$ supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS Attractor solutions correspond to the vanishing determinant of a (fermionic) gaugino mass matrix. The stability of these solutions is controlled by the data of the underlying Special K\"{a}hler Geometry of the vector multiplets' moduli space. Finally, after analyzing the 1-modulus case more in detail, we briefly comment on the choice of the K\"{a}hler gauge and its relevance for the recently discussed entropic functional.

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