Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)

Abstract

In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a brief overview of charged black holes in supergravity and string theory, we give an extensive introduction to special and very special geometry, attractor flows and topological string theory, including holomorphic anomalies. We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates microscopic degeneracies to the topological string amplitude, and review precision tests of this formula on ``small'' black holes. Finally, motivated by a holographic interpretation of the OSV conjecture, we give a systematic approach to the radial quantization of BPS black holes (i.e. quantum attractors). This suggests the existence of a one-parameter generalization of the topological string amplitude, and provides a general framework for constructing automorphic partition functions for black hole degeneracies in theories with sufficient degree of symmetry.

103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important upgrade, prepared for the proceedings of Frascati School on Attractor Mechanism; Sec 7 was largely rewritten to incorporate recent progress; more figures, more refs, and minor changes in abstract and introduction

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• Counting Dyons in N=4 String Theory
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• Two Dimensional QCD is a String Theory
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• Topological Amplitudes in String Theory
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• AdS2 Quantum Gravity and String Theory
• New Connections Between 4D and 5D Black Holes
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• R^4 Couplings in M and Type II Theories
• Precision Counting of Small Black Holes
• Non-Supersymmetric Attractors in String Theory
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
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• The Symplectic Structure of N=2 Supergravity and its Central Extension
• Chern-Simons Theory and Topological Strings
• Increase of Black Hole Entropy in Higher Curvature Gravity
• Macroscopic entropy formulae and non-holomorphic corrections for supersymmetric black holes
• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• E(7) Symmetric Area of the Black Hole Horizon
• A Stringy Cloak for a Classical Singularity
• The Non-BPS Black Hole Attractor Equation
• New Attractors
• General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus
• Counting higher genus curves in a Calabi-Yau manifold
• N=2 Type II- Heterotic duality and Higher derivative F-terms
• Conformal and Quasiconformal Realizations of Exceptional Lie Groups
• Black hole partition functions and duality
• Dyon Spectrum in CHL Models
• The quantum structure of black holes
• Internal Structure of Black Holes
• Fivebrane Instantons and $R^2$ couplings in $N=4$ String Theory
• Exact and Asymptotic Degeneracies of Small Black Holes
• Strings, Black Holes, and Quantum Information
• Fermions from Half-BPS Supergravity
• D1-D5 black hole microstate counting from supergravity
• Schwinger pair production in AdS2
• Duality and Moduli Spaces for Time-Like Reductions
• Stringy Black Holes and the Geometry of Entanglement
• Minimal representations, spherical vectors, and exceptional theta series I
• Exact Black Hole Degeneracies and the Topological String
• Hamiltonian Formalism for Black Holes and Quantization
• Area law corrections from state counting and supergravity
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• Black Holes, Elementary Strings and Holomorphic Anomaly
• Geometry Quantization from Supergravity: the case of "Bubbling AdS"
• Quantum Cosmology and Conformal Invariance
• Topological Sigma-Models in Four Dimensions and Triholomorphic Maps
• Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
• Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds
• Gauge theory, topological strings, and S-duality
• $R^4$ couplings, the fundamental membrane and exceptional theta correspondences
• Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups
• The Automorphic Membrane
• Black holes and Elementary String States in N=2 Supersymmetric String Theories
• Supersymmetry and First Order Equations for Extremal States: Monopoles, Hyperinstantons, Black-Holes and p-Branes
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• Quantization of the Reissner-Nordström Black Hole

Cited by in corpus (72)

• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Split States, Entropy Enigmas, Holes and Halos
• Instabilities of Black Strings and Branes
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Black Holes, Qubits and Octonions
• Generating Geodesic Flows and Supergravity Solutions
• String Theory Effects on Five-Dimensional Black Hole Physics
• First Order Description of Black Holes in Moduli Space
• Black holes admitting a Freudenthal dual
• Extremal black holes, nilpotent orbits and the true fake superpotential
• 5D Black Holes and Strings with Higher Derivatives
• Twistors and Black Holes
• $R^4$ couplings and automorphic unipotent representations
• Quantum Attractor Flows
• Erice Lectures on Black Holes and Attractors
• BPS Black Holes
• Non-supersymmetric Black Holes and Topological Strings
• Precision Entropy of Spinning Black Holes
• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• Eisenstein series and automorphic representations
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• Freudenthal triple classification of three-qubit entanglement
• 4d/5d Correspondence for the Black Hole Potential and its Critical Points
• 5D Attractors with Higher Derivatives
• Critical points of the Black-Hole potential for homogeneous special geometries
• Black-Hole Attractors in N=1 Supergravity
• Attractors in Black
• Black Hole Entropy and Finite Geometry
• BPS Black Hole Horizons in N=2 Gauged Supergravity
• Emergence of Species Scale Black Hole Horizons
• A One Parameter Family of Calabi-Yau Manifolds with Attractor Points of Rank Two
• Effects of brane-flux transition on black holes in string theory
• Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
• Large D-instanton effects in string theory
• Quantum covariant c-map
• Integrability of Supergravity Black Holes and New Tensor Classifiers of Regular and Nilpotent Orbits
• Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity
• Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
• Crystal Melting and Wall Crossing Phenomena
• 5D Black Holes and Non-linear Sigma Models
• Extremal black holes in D=5: SUSY vs. Gauss-Bonnet corrections
• alpha'^2-corrections to extremal dyonic black holes in heterotic string theory
• Arrow of Time in String Theory
• Generalized Einstein Operator Generating Functions
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• On Extremal Limits and Duality Orbits of Stationary Black Holes
• Black Hole Meiosis
• Extremal Limits of Rotating Black Holes
• On the Entropy of Four-Dimensional Near-Extremal N=2 Black Holes with R^2-Terms
• A Note on Exact Solutions and Attractor Mechanism for Non-BPS Black Holes
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Black Hole Giants
• Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• Rotating black holes, global symmetry and first order formalism
• Conformal TBA for resolved conifolds
• Cargese lectures on string theory with eight supercharges
• Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
• Functional determinants, index theorems, and exact quantum black hole entropy
• Nilpotent orbits in real symmetric pairs and stationary black holes
• Topological Quantum Statistical Mechanics and Topological Quantum Field Theories
• (p,q)-form Kaehler Electromagnetism
• Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality
• Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
• Stationary $D=4$ Black Holes in Supergravity: The Issue of Real Nilpotent Orbits
• Smarr Mass formulas for BPS multicenter Black Holes
• Supersymmetric black rings and non-linear sigma models
• Attractor Flows in st^2 Black Holes
• On Symmetries of Extremal Black Holes with One and Two Centers
• Scalar Moduli, Wall Crossing and Phenomenological Predictions
• On Real Intrinsic Wall Crossings
• On Attractor Flow and Small Black Holes