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Abstract: Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as aholographic correspondence in the mini-superspace approximation, we study theradial quantization of stationary, spherically symmetric black holes in fourdimensions. A key ingredient is the classical equivalence between the radialevolution equation and geodesic motion of a fiducial particle on the modulispace M^* 3 of the three-dimensional theory after reduction along the timedirection. In the case of N=2 supergravity, M^* 3 is a para-quaternionic-Kahlermanifold; in this case, we show that BPS black holes correspond to a particularclass 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 theBPS phase space in terms of the sheaf cohomology of Z, and compute the exactwave function of a BPS black hole with fixed electric and magnetic charges inthis framework. We comment on the relation to the topological string amplitude,extensions to N>2 supergravity theories, and applications to automorphic blackhole partition functions.



Author: Murat Gunaydin, Andrew Neitzke, Boris Pioline, Andrew Waldron

Source: https://arxiv.org/







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