Lectures on Quantum Black Holes

Abstract

In these notes we describe recent progress in understanding finite size corrections to the black hole entropy. Much of the earlier work concerning quantum black holes has been in the limit of large charges when the area of the even horizon is also large. In recent years there has been substantial progress in understanding the entropy of supersymmetric black holes within string theory going well beyond the large charge limit. It has now become possible to begin exploring finite size effects in perturbation theory in inverse size and even nonperturbatively, with highly nontrivial agreements between thermodynamics and statistical mechanics. Unlike the leading Bekenstein-Hawking entropy which follows from the two-derivative Einstein-Hilbert action, these finite size corrections depend sensitively on the phase under consideration and contain a wealth of information about the details of compactification as well as the spectrum of nonperturbative states in the theory. Finite-size corrections are therefore very interesting as a valuable window into the microscopic degrees of freedom of the quantum theory.

79 pages, based on lectures given at the summer school 'Strings and Fundamental. Physics 2010' in Munich

References in corpus (40)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• N=2 Extremal Black Holes
• Supersymmetry and Attractors
• D--branes and Spinning Black Holes
• Macroscopic Entropy of $N=2$ Extremal Black Holes
• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Applied Conformal Field Theory
• Dyon - Monopole Bound States, Self-Dual Harmonic Forms on the Multi-Monopole Moduli Space, and SL(2,Z) Invariance in String Theory
• EXTREMAL BLACK HOLES AND ELEMENTARY STRING STATES
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Exact Counting of Black Hole Microstates
• Corrections to macroscopic supersymmetric black-hole entropy
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Black Hole Solutions in Heterotic String Theory on a Torus
• Microscopic Black Hole Entropy in Theories with Higher Derivatives
• Holographic Gravitational Anomalies
• Precision Counting of Small Black Holes
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• A Stringy Cloak for a Classical Singularity
• Asymptotic degeneracy of dyonic N=4 string states and black hole entropy
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Comments on the Spectrum of CHL Dyons
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Exact and Asymptotic Degeneracies of Small Black Holes
• Dying Dyons Don't Count
• New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!
• Stationary BPS Solutions in N=2 Supergravity with R^2-Interactions
• 5D Black Rings and 4D Black Holes
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Area law corrections from state counting and supergravity
• Re-Recounting Dyons in N=4 String Theory
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• Genus Two Surface and Quarter BPS Dyons: The Contour Prescription
• Quantum entropy of supersymmetric black holes

Cited by in corpus (75)

• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• The AdS/CFT Correspondence
• F-Theory, Spinning Black Holes and Multi-string Branches
• Behavior of Quasinormal Modes and high dimension RN-AdS Black Hole phase transition
• Benefits of Objective Collapse Models for Cosmology and Quantum Gravity
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• The Kerr/CFT correspondence and its extensions: a comprehensive review
• Resurgence in complex Chern-Simons theory
• Dynamics for a 2-vertex Quantum Gravity Model
• Indefinite theta series and generalized error functions
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• Emergence of Species Scale Black Hole Horizons
• Fricke S-duality in CHL models
• Holomorphic projections and Ramanujan's mock theta functions
• The Cheshire Cap
• Evidence for galaxy dynamics tracing background cosmology below the de Sitter scale of acceleration
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Modular discretization of the AdS2/CFT1 Holography
• Eichler-Selberg Type Identities for Mixed Mock Modular Forms
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• The Bailey chain and mock theta functions
• Quantum black hole entropy and the holomorphic prepotential of N=2 supergravity
• Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
• Small Black Hole Explosions
• Vafa-Witten theory and iterated integrals of modular forms
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Curvature squared action in four dimensional $N=2$ supergravity using the dilaton Weyl multiplet
• Black Holes with Intrinsic Spin
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• Quantum Thermodynamics of a Quantum Sized AdS Black Hole
• Anomalies as Obstructions: from Dimensional Lifts to Swampland
• Black Holes as Conformal Field Theories on Horizons
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Gliner Vacuum, Self-consistent Theory of Ruppeiner Geometry for Regular Black Holes
• Two critical phenomena in the exactly soluble quantized Schwarzschild black hole
• The quantum cat map on the modular discretization of extremal black hole horizons
• The Hodge-elliptic genus, spinning BPS states, and black holes
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• Dyon degeneracies from Mathieu moonshine
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes
• Boundary conditions and localization on AdS: Part 2 General analysis
• Non-extremal black hole solutions from the c-map
• The Holar Wind
• Properties of dyons in $\mathcal{N}=4$ theories at small charges
• Quantum entropy of BMPV black holes and the topological M-theory conjecture
• Thermodynamic Geometry and Phase Transitions of AdS Braneworld Black Holes
• Remarks on distinguishability of Schwarzschild spacetime and thermal Minkowski spacetime using Resonance Casimir-Polder interaction
• Extremal Black Hole Entropy from Horizon Conformal Field Theories
• A Generalised Garfinkle-Vachaspati Transform
• How the mass of a scalar field influences Resonance Casimir-Polder interaction in Schwarzschild spacetime
• On the sigma-model of deformed special geometry
• Polar harmonic Maaß forms and holomorphic projection
• $S$-Functions, Spectral Functions of Hyperbolic Geometry, and Vertex Operators with Applications to Structure for Weyl and Orthogonal Group Invariants
• An approach to BPS black hole microstate counting in an N=2 STU model
• Horizon states and the sign of their index in $\mathcal{N}=4$ dyons
• Three Avatars of Mock Modularity
• Generating new $N=2$ small black holes
• Generalised Garfinkle-Vachaspati Transform With Dilaton
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• Entropy increases at linear order in scalar-hairy Lovelock gravity
• Geometry of Massless Scattering in Integrable Superstring
• Quasimodular forms and sl(m|m)^ characters
• On Exponentially Suppressed Corrections to BMPV Black Hole Entropy
• M5-brane prongs, string soliton bound states and wall-crossing
• Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry
• Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry
• A $p$-arton Model for Modular Cusp Forms
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• At the End of the World: Local Dynamical Cobordism
• Geobiodynamics and Roegenian Economic Systems
• Probing the Purely Ingoing Nature of the Black-hole Event Horizon
• First Law of Black Hole in the Gravitational Electromagnetic System
• Partition functions for supersymmetric gauge theories on spheres
• Equivariant and supersymmetric localization in QFT
• A Scenario for Strong Gravity in Particle Physics: An alternative mechanism for black holes to appear at accelerator experiments