Charge Orbits of Symmetric Special Geometries and Attractors

Details Charge Orbits of Symmetric Special Geometries and Attractors Charge Orbits of Symmetric Special Geometries and Attractors

2006-06-21

arxiv.org/abs/hep-th/0606209v2

Int.J.Mod.Phys.A21:5043-5098,2006

Physics

High Energy Physics

High Energy Physics - Theory

63 pages, 9 Tables. v2: typos fixed, Refs. added, accepted for publication in IJMPA

Scientific paper

10.1142/S0217751X06034355

We study the critical points of the black hole scalar potential $V_{BH}$ in N=2, d=4 supergravity coupled to $n_{V}$ vector multiplets, in an asymptotically flat extremal black hole background described by a 2(n_{V}+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special K\"{a}hler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(n_{V}+1)-dimensional representation $R_{V}$ of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The three species of solutions to the N=2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of $V_{BH}$ and some group theoretical considerations on homogeneous symmetric special K\"{a}hler geometry.

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