Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model

Abstract

Motivated by recent advances in Donaldson-Thomas theory, four-dimensional $\mathcal{N}=4$ string-string duality is examined in a reduced rank theory on a less studied BPS sector. In particular we identify candidate partition functions of "untwisted" quarter-BPS dyons in the heterotic ${\mathbb{Z}}_2$ CHL model by studying the associated chiral genus two partition function, based on the M-theory lift of string webs argument by Dabholkar and Gaiotto. This yields meromorphic Siegel modular forms for the Iwahori subgroup $B(2)\subset {\text{Sp}}_4(\mathbb{Z})$ which generate BPS indices for dyons with untwisted sector electric charge, in contrast to twisted sector dyons counted by a multiplicative lift of twisted-twining elliptic genera known from Mathieu moonshine. The new partition functions are shown to satisfy the expected constraints coming from wall-crossing and S-duality symmetry as well as the black hole entropy based on the Gauss-Bonnet term in the effective action. In these aspects our analysis confirms and extends work of Banerjee, Sen and Srivastava, which only addressed a subset of the untwisted sector dyons considered here. Our results are also compared with recently conjectured formulae of Bryan and Oberdieck for the partition functions of primitive DT invariants of the CHL orbifold $X=(\text{K3}\times T^2)/{\mathbb{Z}}_2$, as suggested by string duality with type IIA theory on $X$.

arXiv comment67 pages, no figures. Revised version, published by JHEP

References in corpus (101)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• D--branes and Spinning Black Holes
• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
• Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams
• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Supergravity flows and D-brane stability
• Automorphic forms with singularities on Grassmannians
• Counting Dyons in N=4 String Theory
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Solitonic Strings and BPS Saturated Dyonic Black Holes
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Notes on the K3 Surface and the Mathieu group M_24
• Exact solutions for supersymmetric stationary black hole composites
• Second-Quantized Mirror Symmetry
• Split States, Entropy Enigmas, Holes and Halos
• Quantum Quivers and Hall/Hole Halos
• Some Relationships Between Dualities in String Theory
• Maximally Supersymmetric String Theories in D<10
• Precision Counting of Small Black Holes
• The Heterotic String is a Soliton
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• STRING STRING DUALITY CONJECTURE IN SIX DIMENSIONS AND CHARGED SOLITONIC STRINGS
• Entropy Function for Heterotic Black Holes
• String Network
• Strong/Weak Coupling Duality from the Dual String
• Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity
• Moduli Space of CHL Strings
• Note on Twisted Elliptic Genus of K3 Surface
• Lectures on Quantum Black Holes
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Mathieu twining characters for K3
• 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
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Split attractor flows and the spectrum of BPS D-branes on the Quintic
• A Note on Toroidal Compactifications of the Type I Superstring and Other Superstring Vacuum Configurations with 16 Supercharges
• Arithmetic of Quantum Entropy Function
• Type IIA-Heterotic Duals With Maximal Supersymmetry
• A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6
• Fivebrane Instantons and $R^2$ couplings in $N=4$ String Theory
• Product Representation of Dyon Partition Function in CHL Models
• A Farey tale for N=4 dyons
• F-Theory, Spinning Black Holes and Multi-string Branches
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Exact Gravitational Threshold Correction in the FHSV Model
• On Type IIB Vacua With Varying Coupling Constant
• Black Holes, Elementary Strings and Holomorphic Anomaly
• Type IIA Dual of the Six-Dimensional CHL Compactification
• Two Centered Black Holes and N=4 Dyon Spectrum
• Mathieu Moonshine in the elliptic genus of K3
• F^4 Terms in N=4 String Vacua
• Spectrum of CHL Dyons from Genus-Two Partition Function
• Partition Functions of Torsion >1 Dyons in Heterotic String Theory on T^6
• Microscopic and Macroscopic Entropy of Extremal Black Holes in String Theory
• Generalities of Quarter BPS Dyon Partition Function and Dyons of Torsion Two
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Black Hole Microstate Counting and its Macroscopic Counterpart
• Holomorphic anomaly equations and the Igusa cusp form conjecture
• Logarithmic Corrections to $N\ge 2$ Black Hole Entropy
• Counting all dyons in N =4 string theory
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• A Note on the Geometry of CHL Heterotic Strings
• The Siegel modular forms of genus 2 with the simplest divisor
• Discrete Information from CHL Black Holes
• Counting BPS states on the Enriques Calabi-Yau
• BKM Lie superalgebras from counting twisted CHL dyons
• No entropy enigmas for N=4 dyons
• Wall Crossing Formula for N=4 Dyons: A Macroscopic Derivation
• Momentum Lattice for CHL String
• 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
• Logarithmic Corrections to Extremal Black Hole Entropy in N = 2, 4 and 8 Supergravity
• Genus Two Surface and Quarter BPS Dyons: The Contour Prescription
• Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Orientifold and F-theory Duals of CHL Strings
• Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
• Mixed Rademacher and BPS Black Holes
• Dyonic black hole degeneracies in $\mathcal{N}=4$ string theory from Dabholkar-Harvey degeneracies
• Topological Amplitudes in Heterotic Strings with Wilson Lines
• Heat Kernels on the AdS(2) cone and Logarithmic Corrections to Extremal Black Hole Entropy
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Dyon degeneracies from Mathieu moonshine
• Dualities in CHL-Models
• Calabi-Yau Duals for CHL Strings
• Heterotic sigma models on $T^8$ and the Borcherds automorphic form ${\Phi }_{12}$
• 3D String Theory and Umbral Moonshine
• Perturbative tests of non-perturbative counting
• Properties of dyons in $\mathcal{N}=4$ theories at small charges
• Mock modularity from black hole scattering states
• Nikulin involutions and the CHL string
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• A Geometric Derivation of the Dyon Wall-Crossing Group

Cited by in corpus (1)

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