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.
|Original language||English (US)|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - 2006|
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)