Product Representation of Dyon Partition Function in CHL Models

Abstract

A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2,Z). In this paper we propose product formulae for these modular forms. This generalizes the result of Borcherds and Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2,Z) group.

LaTeX file, 39 pages; minor changes

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Cited by in corpus (78)

• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
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• Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates
• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
• Note on Twisted Elliptic Genus of K3 Surface
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Comments on the Spectrum of CHL Dyons
• Supersymmetric Index from Black Hole Entropy
• Dying Dyons Don't Count
• Dyon Spectrum in N=4 Supersymmetric Type II String Theories
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• alpha'-Corrections to Extremal Dyonic Black Holes in Heterotic String Theory
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Two Centered Black Holes and N=4 Dyon Spectrum
• Mathieu Moonshine in the elliptic genus of K3
• Spectrum of CHL Dyons from Genus-Two Partition Function
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two
• Black Hole Microstate Counting and its Macroscopic Counterpart
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• Counting all dyons in N =4 string theory
• Recounting Dyons in N=4 String Theory
• Discrete Information from CHL Black Holes
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• BKM Lie superalgebras from counting twisted CHL dyons
• No entropy enigmas for N=4 dyons
• Fricke S-duality in CHL models
• How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
• A Twist in the Dyon Partition Function
• Rare Decay Modes of Quarter BPS Dyons
• S-duality Action on Discrete T-duality Invariants
• Unravelling Mathieu Moonshine
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Adding Charges to N=4 Dyons
• Extremal black holes in D=5: SUSY vs. Gauss-Bonnet corrections
• alpha'^2-corrections to extremal dyonic black holes in heterotic string theory
• Generalized Kac-Moody Algebras from CHL dyons
• On the dyon partition function in N=2 theories
• Genus Two Surface and Quarter BPS Dyons: The Contour Prescription
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Negative discriminant states in N=4 supersymmetric string theories
• Dyon Death Eaters
• Degeneracy of Decadent Dyons
• Three String Junction and N=4 Dyon Spectrum
• Logarithmic Corrections to Twisted Indices from the Quantum Entropy Function
• Subleading Correction to Statistical Entropy for BMPV Black Hole
• Mixed Rademacher and BPS Black Holes
• Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Borcherds Algebras and N=4 Topological Amplitudes
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Heterotic string on the CHL orbifold of K3
• Supersymmetrization of deformed BMS algebras
• Dualities in CHL-Models
• Dyon degeneracies from Mathieu moonshine
• $\mathcal{N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$
• Properties of dyons in $\mathcal{N}=4$ theories at small charges
• BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• Twisted elliptic genus for K3 and Borcherds product
• On Mathieu moonshine and Gromov-Witten invariants
• Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N}=4$ CHL models
• An approach to BPS black hole microstate counting in an N=2 STU model
• Generating new $N=2$ small black holes
• Black Hole Hair Removal For N=4 CHL Models
• Horizon states and the sign of their index in $\mathcal{N}=4$ dyons
• A Geometric Derivation of the Dyon Wall-Crossing Group
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• Mock Modularity In CHL Models
• On Exponentially Suppressed Corrections to BMPV Black Hole Entropy
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Mock Modularity Of Twisted Index In CHL Models