BPS black holes, quantum attractor flows and automorphic forms

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.

9 pages, revtex; v2: references added and typos corrected

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Cited by in corpus (57)

• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Universal BPS structure of stationary supergravity solutions
• Generating Geodesic Flows and Supergravity Solutions
• The black-hole/qubit correspondence: an up-to-date review
• Hypermultiplets and Topological Strings
• Twistors and Black Holes
• $R^4$ couplings and automorphic unipotent representations
• Quantum Attractor Flows
• First-order flow equations for extremal and non-extremal black holes
• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• Topological wave functions and heat equations
• Eisenstein series and automorphic representations
• Extremal solutions of the S3 model and nilpotent orbits of G2(2)
• Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
• First-order flows and stabilisation equations for non-BPS extremal black holes
• The full integration of black hole solutions to symmetric supergravity theories
• Multi-black holes from nilpotent Lie algebra orbits
• A Unified Approach to the Minimal Unitary Realizations of Noncompact Groups and Supergroups
• Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
• Freudenthal Dual Lagrangians
• Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
• BRST Detour Quantization
• Black Hole Nilpotent Orbits and Tits Satake Universality Classes
• Cancellation of divergences up to three loops in exceptional field theory
• Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Jordan C*-Algebras and Supergravity
• Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
• Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• The attractor mechanism as a distillation procedure
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Arithmetic and Hyperbolic Structures in String Theory
• Maurer-Cartan Equations and Black Hole Superpotentials in N =8 Supergravity
• Extremal Black Holes as Qudits
• 1/8 BPS black hole composites
• Black holes and equivariant charge vectors in N=2,d=4 supergravity
• N=4 BPS black holes and octonionic twistors
• SU(2) deformations of the minimal unitary representation of OSp(8*|2N) as massless 6D conformal supermultiplets
• Nilpotent orbits in real symmetric pairs and stationary black holes
• Non-Supersymmetric Attractors in Symmetric Coset Spaces
• Instantons and Wormholes in N=2 supergravity
• All extremal instantons in Einstein-Maxwell-dilaton-axion theory
• Time-like reductions of five-dimensional supergravity
• Black Holes and Higher Composition Laws
• A Comment on Quantum Distribution Functions and the OSV Conjecture
• Non-extremal black holes from the generalised r-map
• First-order attractor flow equations for supersymmetric black rings in N=2, D=5 supergravity
• Extremal black holes and nilpotent orbits
• Stationary $D=4$ Black Holes in Supergravity: The Issue of Real Nilpotent Orbits
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Supersymmetric black rings and non-linear sigma models
• On Dimensional Reduction of Magical Supergravity Theories
• On an Algebraic Structure of Dimensionally Reduced Magical Supergravity Theories
• On Real Intrinsic Wall Crossings
• U-Duality and the Leech Lattice
• Towards the Core of the Quantum Monopole