### Abstract

We study the critical points of the black hole scalar potential V _{BH} in N = 2, d = 4 super-gravity 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 Kähler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing 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 nondegenerate, namely they have nonvanishing 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 Kähler geometry.

Original language | English (US) |
---|---|

Pages (from-to) | 5043-5097 |

Number of pages | 55 |

Journal | International Journal of Modern Physics A |

Volume | 21 |

Issue number | 25 |

DOIs | |

State | Published - Oct 10 2006 |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics

### Cite this

*International Journal of Modern Physics A*,

*21*(25), 5043-5097. https://doi.org/10.1142/S0217751X06034355

}

*International Journal of Modern Physics A*, vol. 21, no. 25, pp. 5043-5097. https://doi.org/10.1142/S0217751X06034355

**Charge orbits of symmetric special geometries and attractors.** / Bellucci, Stefano; Ferrara, Sergio; Günaydin, Murat; Marrani, Alessio.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Charge orbits of symmetric special geometries and attractors

AU - Bellucci, Stefano

AU - Ferrara, Sergio

AU - Günaydin, Murat

AU - Marrani, Alessio

PY - 2006/10/10

Y1 - 2006/10/10

N2 - We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 super-gravity coupled to nV vector multiplets, in an asymptotically flat extremal black hole background described by a 2(nV + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(nV + 1)-dimensional representation RV of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing 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 VBH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

AB - We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 super-gravity coupled to nV vector multiplets, in an asymptotically flat extremal black hole background described by a 2(nV + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(nV + 1)-dimensional representation RV of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing 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 VBH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

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U2 - 10.1142/S0217751X06034355

DO - 10.1142/S0217751X06034355

M3 - Article

AN - SCOPUS:33750434304

VL - 21

SP - 5043

EP - 5097

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 25

ER -