Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N}=4$ CHL models

Abstract

We use continued fractions to perform a systematic and explicit characterization of the decays of two-centred dyonic black holes in $4D$ $\mathcal{N}=4$ heterotic ${\mathbb{Z}}_N$ CHL models. Thereby we give a new exact solution for the problem of counting decadent dyons in these models.

arXiv comment32 pages, 4 figures

References in corpus (34)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Counting Dyons in N=4 String Theory
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Maximally Supersymmetric String Theories in D<10
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Arithmetic and Attractors
• Moduli Space of CHL Strings
• Counting BPS Blackholes in Toroidal Type II String Theory
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Dual String Pairs With N=1 And N=2 Supersymmetry In Four Dimensions
• Comments on the Spectrum of CHL Dyons
• Dyon Spectrum in CHL Models
• Type IIA-Heterotic Duals With Maximal Supersymmetry
• Arithmetic of Quantum Entropy Function
• Product Representation of Dyon Partition Function in CHL Models
• Dying Dyons Don't Count
• Type IIA Dual of the Six-Dimensional CHL Compactification
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Attractors and Arithmetic
• Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
• Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two
• Counting all dyons in N =4 string theory
• How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• On walls of marginal stability in N=2 string theories
• Negative discriminant states in N=4 supersymmetric string theories
• Degeneracy of Decadent Dyons
• Mixed Rademacher and BPS Black Holes
• 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
• Properties of dyons in $\mathcal{N}=4$ theories at small charges
• Black Holes and Higher Composition Laws
• Black Hole Bound State Metamorphosis
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model

Cited by in corpus (3)

• The gravitational path integral for $N=4$ BPS black holes from black hole microstate counting
• Rademacher expansion of a Siegel modular form for $\mathcal{N}=4$ counting
• Black Hole Hair Removal For N=4 CHL Models