### Abstract

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M*_{3} of the three-dimensional theory after reduction along the time direction. In the case of N ≤ 2 supergravity, M*_{3} is a para-quaternionic-Kähler manifold; in this case, we show that BPS black holes correspond to a particular class of geodesics which lift holomorphically to the twistor space Z of M*_{3}, and identify Z as the BPS phase space. We give a natural quantization of the BPS phase space in terms of the sheaf cohomology of Z, and compute the exact wave function of a BPS black hole with fixed electric and magnetic charges in this framework. We comment on the relation to the topological string amplitude, extensions to N > 2 supergravity theories, and applications to automorphic black hole partition functions.

Original language | English (US) |
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Article number | 056 |

Journal | Journal of High Energy Physics |

Volume | 2007 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2007*(9), [056]. https://doi.org/10.1088/1126-6708/2007/09/056