A Farey tale for N=4 dyons

Abstract

We study exponentially suppressed contributions to the degeneracies of extremal black holes. Within Sen's quantum entropy function framework and focusing on extremal black holes with an intermediate AdS3 region, we identify an infinite family of semi-classical AdS2 geometries which can contribute effects of order exp(S_0/c), where S_0 is the Bekenstein-Hawking-Wald entropy and c is an integer greater than one. These solutions lift to the extremal limit of the SL(2,Z) family of BTZ black holes familiar from the "black hole Farey tail". We test this understanding in N=4 string vacua, where exact dyon degeneracies are known to be given by Fourier coefficients of Siegel modular forms. We relate the sum over poles in the Siegel upper half plane to the Farey tail expansion, and derive a "Farey tale" expansion for the dyon partition function. Mathematically, this provides a (formal) lift from Hilbert modular forms to Siegel modular forms with a pole at the diagonal divisor.

31 pages

References in corpus (33)

• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Geometry of the 2+1 Black Hole
• AdS3 Black Holes and a Stringy Exclusion Principle
• Black Hole Entropy in M-Theory
• The (2+1)-Dimensional Black Hole
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Mock Theta Functions
• Counting Dyons in N=4 String Theory
• AdS2 Quantum Gravity and String Theory
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Supersymmetry of the 2+1 black holes
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• A Black Hole Farey Tail
• Vacuum States for AdS_2 Black Holes
• 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
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Arithmetic of Quantum Entropy Function
• Fivebrane Instantons and $R^2$ couplings in $N=4$ String Theory
• Holographic Description of AdS_2 Black Holes
• R^2 Corrections and Non-perturbative Dualities of N=4 String ground states
• Partition functions and elliptic genera from supergravity
• The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras
• Exact Black Hole Degeneracies and the Topological String
• Ads(3)/CFT(2) to Ads(2)/CFT(1)
• Spectrum of CHL Dyons from Genus-Two Partition Function
• Re-Recounting Dyons in N=4 String Theory
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Corrections to the statistical entropy of five dimensional black holes
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Subleading Correction to Statistical Entropy for BMPV Black Hole

Cited by in corpus (59)

• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Nonperturbative black hole entropy and Kloosterman sums
• Quantum black holes, localization and the topological string
• Supersymmetric Index from Black Hole Entropy
• The asymptotic growth of states of the 4d N=1 superconformal index
• State Operator Correspondence and Entanglement in AdS_2/CFT_1
• Interpreting Single Jet Measurements in Pb+Pb Collisions at the LHC
• All solutions of the localization equations for N=2 quantum black hole entropy
• A de Sitter Farey Tail
• Supersymmetry, Localization and Quantum Entropy Function
• Black Hole Microstate Counting and its Macroscopic Counterpart
• Non-Pertubative Quantum Corrections to a Born-Infeld Black Hole and its Information Geometry
• Discrete Information from CHL Black Holes
• Arithmetic of N=8 Black Holes
• How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
• Beyond Logarithmic Corrections to Cardy Formula
• Parton shower evolution in medium and nuclear modification of photon-tagged jets in Pb+Pb collisions at the LHC
• A Twist in the Dyon Partition Function
• BRST quantization and equivariant cohomology: localization with asymptotic boundaries
• Quantum black hole entropy and the holomorphic prepotential of N=2 supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• Quantum Work and Information Geometry of a Quantum Myers-Perry Black Hole
• Quantum Corrections to the Thermodynamics of Black Branes
• Quantum Thermodynamics of an ${\alpha }^{\prime }$-Corrected Reissner-Nordström Black Hole
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Negative discriminant states in N=4 supersymmetric string theories
• Quantum Thermodynamics of an M2-M5 Brane System
• Mixed Rademacher and BPS Black Holes
• Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
• Dyonic black hole degeneracies in $\mathcal{N}=4$ string theory from Dabholkar-Harvey degeneracies
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Perturbative tests of non-perturbative counting
• The gravitational index of 5d black holes and black strings
• Functional determinants, index theorems, and exact quantum black hole entropy
• Properties of dyons in $\mathcal{N}=4$ theories at small charges
• On the microstructure of higher-dimensional Reissner-Nordström black holes in quantum regime
• The gravitational path integral for $N=4$ BPS black holes from black hole microstate counting
• Mock modularity from black hole scattering states
• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• Rademacher Sums and Rademacher Series
• Stringy effects in black hole decay
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Rademacher expansion of a Siegel modular form for $\mathcal{N}=4$ counting
• Quantum entropy of supersymmetric black holes
• Generalized Kloosterman Sums from M2-branes
• Quantum Modular $\hat{Z}{}^G$-Invariants
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• The topologically twisted index of $\mathcal{N}=4$ SU($N$) Super-Yang-Mills theory and a black hole Farey tail
• On the localization manifold of 5d supersymmetric spinning black holes
• Exact holography and black hole entropy in N=8 and N=4 string theory
• U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• On the exact entropy of $\mathcal{N}=2$ black holes
• Mock Modularity Of Twisted Index In CHL Models