Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-07-02
JHEP 0709:056,2007
Physics
High Energy Physics
High Energy Physics - Theory
43 pages, 6 figures; v2: typos and references added; v3: published version, minor changes
Scientific paper
10.1088/1126-6708/2007/09/056
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-Kahler 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.
Gunaydin Murat
Neitzke Andrew
Pioline Boris
Waldron Andrew
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