A Black Hole Farey Tail

Abstract

We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity.

54 pages, harvmac b-mode. 9 figures; minor mistakes corrected; V3: An important mistake has been corrected. Conclusions essentially unchanged

References in corpus (2)

• Supersymmetric Conical Defects: Towards a string theoretic description of black hole formation
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity

Cited by in corpus (118)

• Eternal Black Holes in AdS
• Entanglement Renyi entropies in holographic theories
• Quantum Gravity Partition Functions in Three Dimensions
• Towards a holographic dual of large-N_c QCD
• Logarithmic Corrections to Black Hole Entropy from the Cardy Formula
• Three-Dimensional Gravity Revisited
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• The complete superconformal index for N=6 Chern-Simons theory
• Microscopic Black Hole Entropy in Theories with Higher Derivatives
• Higher Spin Black Holes
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Precision Counting of Small Black Holes
• Chiral Gravity, Log Gravity and Extremal CFT
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• A Farey Tail for Attractor Black Holes
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Higher Spin Black Holes from CFT
• Nonperturbative black hole entropy and Kloosterman sums
• Instability of non-supersymmetric smooth geometries
• An Exact Black Hole Entropy Bound
• Baby Universes in String Theory
• Lightcone Modular Bootstrap and Pure Gravity
• Black hole bound states in AdS_3 x S^2
• String Theory Effects on Five-Dimensional Black Hole Physics
• Dying Dyons Don't Count
• Relaxation in Conformal Field Theory, Hawking-Page Transition, and Quasinormal/Normal Modes
• The Gravity Dual of the Ising Model
• Les Houches Lectures on Strings and Arithmetic
• 2D CFT Partition Functions at Late Times
• F-Theory, Spinning Black Holes and Multi-string Branches
• A Farey tale for N=4 dyons
• Summing over Geometries in String Theory
• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• M-theory and a Topological String Duality
• Exciting AdS Orbifolds
• BPS Black Hole Degeneracies and Minimal Automorphic Representations
• Hiding the cosmological constant
• Ads(3)/CFT(2) to Ads(2)/CFT(1)
• Twistor Approach to String Compactifications: a Review
• PyCFTBoot: A flexible interface for the conformal bootstrap
• A de Sitter Farey Tail
• Phase transitions in symmetric orbifold CFTs and universality
• One-Loop BPS amplitudes as BPS-state sums
• Bose-Fermi duality and entanglement entropies
• D3-instantons, Mock Theta Series and Twistors
• Moulting Black Holes
• Warped Weyl fermion partition functions
• Corrections to the statistical entropy of five dimensional black holes
• Near Horizon Limits of Massless BTZ and Their CFT Duals
• Harmonic analysis of 2d CFT partition functions
• Restoring Unitarity in BTZ Black Hole
• Two Charge System Revisited: Small Black Holes or Horizonless Solutions?
• Rademacher Expansions and the Spectrum of 2d CFT
• Higher Spin Theories in AdS_3 and a Gravitational Exclusion Principle
• Lectures on black holes and the AdS_3 / CFT_2 correspondence
• Phases of Holographic Interfaces
• From Conformal Blocks to Path Integrals in the Vaidya Geometry
• Chern-Simons Invariants from Ensemble Averages
• Counting Giant Gravitons in AdS_3
• NGN, QCD_2 and chiral phase transition from string theory
• AdS_3 Partition Functions Reconstructed
• Counting RG flows
• Mock Modular Mathieu Moonshine Modules
• Holographic partition functions and phases for higher genus Riemann surfaces
• Beyond Logarithmic Corrections to Cardy Formula
• Black Holes and Large Order Quantum Geometry
• BTZ Black Hole with Higher Derivatives, the Second Law of Thermodynamics, and Statistical Entropy: A New Proposal
• Phase Transitions in Warped AdS${}_3$ Gravity
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
• Large-N limits of 2d CFTs, Quivers and AdS_3 duals
• Conformal Field Theories with Sporadic Group Symmetry
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity
• An Index for 2D field theories with large N=4 superconformal symmetry
• Extremal black holes, Holography & Coarse graining
• Three Dimensional Origin of AdS_2 Quantum Gravity
• Partition Functions of Three-Dimensional Pure Gravity
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
• Exact Path Integral for 3D Quantum Gravity
• Mixed Rademacher and BPS Black Holes
• Subleading Correction to Statistical Entropy for BMPV Black Hole
• Permutation Orbifolds in the large N Limit
• Microscopic Entropy of AdS${}_3$ Black Holes Revisited
• Black Hole Entropy and the Problem of Universality
• Small Black holes vs horizonless solutions in AdS
• D1/D5 systems in $\mathcal{N}=4$ string theories
• Hagedorn String Thermodynamics in Curved Spacetimes and near Black Hole Horizons
• The theory of vector-modular forms for the modular group
• The Spectra of Supersymmetric States in String Theory
• Relative entropy in higher spin holography
• Exact Path Integral for 3D Higher Spin Gravity
• Rademacher Sums and Rademacher Series
• Echoes in the Kerr/CFT correspondence
• Aspects of Dirichlet S-branes
• Partition Functions of Three-Dimensional Quantum Gravity and the Black Hole Entropy
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Four dimensional Abelian duality and SL(2,Z) action in three dimensional conformal field theory
• Quantum entropy of supersymmetric black holes
• S-duality and a large N phase transition in N=4 SYM on K3 at strong coupling
• Generalized Kloosterman Sums from M2-branes
• Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity
• Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT${}_2$
• Monstrous entanglement
• Umbral Moonshine and String Duality
• N=4 SYM on K3 and the AdS(3)/CFT(2) Correspondence
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• On the space of elliptic genera
• Exact holography and black hole entropy in N=8 and N=4 string theory
• Higher Spin de Sitter Quantum Gravity
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• Exact indices for D-particles, flow trees and the derived category
• U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums
• On the exact entropy of $\mathcal{N}=2$ black holes
• Three-dimensional quantum gravity according to ST modular bootstrap