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Quantum attractor flows
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DOI：10.1088/1126-6708/2007/09/056.png)
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Abstract
En 中文
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 twist or 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.
Keywords:
black holes
black holes in string theory
models of quantum gravity
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