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03 November 2024 

   

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Quantum Attractor Flows  Murat Gunaydin
; Andrew Neitzke
; Boris Pioline
; Andrew Waldron
;  Date: 
2 Jul 2007  Abstract:  Motivated by the interpretation of the OoguriStromingerVafa conjecture as a
holographic correspondence in the minisuperspace 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 threedimensional theory after reduction along the time
direction. In the case of N=2 supergravity, M^*_3 is a paraquaternionicKahler
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.  Source:  arXiv, arxiv.0707.0267  Services:  Forum  Review  PDF  Favorites 


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