BPS black holes, quantum attractor flows, and automorphic forms

Murat Gunaydin, Andrew Neitzke, Boris Pioline, Andrew Waldron

Research output: Contribution to journalArticlepeer-review

89 Scopus citations


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 languageEnglish (US)
Article number084019
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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