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BPS black holes, quantum attractor flows and automorphic forms

Murat Gunaydin·Andrew Neitzke·Boris Pioline·Andrew Waldron
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Abstract

We propose a program for counting microstates of four-dimensional BPS black holes in N >= 2 supergravities with symmetric-space valued scalars by exploiting the symmetries of timelike reduction to three dimensions. Inspired by the equivalence between the four dimensional attractor flow and geodesic flow on the three-dimensional scalar manifold, we radially quantize stationary, spherically symmetric BPS geometries. Connections between the topological string amplitude, attractor wave function, the Ooguri-Strominger-Vafa conjecture and the theory of automorphic forms suggest that black hole degeneracies are counted by Fourier coefficients of modular forms for the three-dimensional U-duality group, associated to special "unipotent" representations which appear in the supersymmetric Hilbert space of the quantum attractor flow.

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Murat Gunaydin, Andrew Neitzke, Boris Pioline, Andrew Waldron. 2006-03-28. BPS black holes, quantum attractor flows and automorphic forms. https://doi.org/10.1103/physrevd.73.084019

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