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arXiv · 0707.0267

Quantum Attractor Flows

Murat Gunaydin·Andrew Neitzke·Boris Pioline·Andrew Waldron
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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-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.

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Murat Gunaydin, Andrew Neitzke, Boris Pioline, Andrew Waldron. 2007-09-23. Quantum Attractor Flows. https://doi.org/10.1088/1126-6708%2F2007%2F09%2F056

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