BKM Lie superalgebras from counting twisted CHL dyons

Abstract

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.

LaTeX, 32 pages; (v2) matches published version

References in corpus (26)

• Black Hole Entropy Function, Attractors and Precision Counting of Microstates
• Counting Dyons in N=4 String Theory
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Exact Counting of Black Hole Microstates
• Notes on the K3 Surface and the Mathieu group M_24
• Precision Counting of Small Black Holes
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• 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
• Mathieu twining characters for K3
• Dyon Spectrum in CHL Models
• Type IIA-Heterotic Duals With Maximal Supersymmetry
• R^2 Corrections and Non-perturbative Dualities of N=4 String ground states
• Exact and Asymptotic Degeneracies of Small Black Holes
• Product Representation of Dyon Partition Function in CHL Models
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Elliptic genus of Calabi-Yau manifolds and Jacobi and Siegel modular forms
• Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
• BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N
• The Siegel modular forms of genus 2 with the simplest divisor
• Discrete Information from CHL Black Holes
• A Twist in the Dyon Partition Function
• Unravelling Mathieu Moonshine
• Generalized Kac-Moody Algebras from CHL dyons
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• The Modular Form of the Barth-Nieto Quintic

Cited by in corpus (24)

• M-strings, Elliptic Genera and N=4 String Amplitudes
• Fricke S-duality in CHL models
• Unravelling Mathieu Moonshine
• Generalised Mathieu Moonshine
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• BKM Lie superalgebras from counting twisted CHL dyons -- II
• Brewing moonshine for Mathieu
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Borcherds Algebras and N=4 Topological Amplitudes
• Dualities in CHL-Models
• Second Quantized Mathieu Moonshine
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• Mathieu Moonshine and Orbifold K3s
• BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• Positivity of discrete information for CHL black holes
• Two moonshines for $L_2(11)$ but none for $M_{12}$
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• Calabi-Yau manifolds and sporadic groups
• Mathieu Moonshine and Siegel Modular Forms
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras
• A non-commuting twist in the partition function
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Mock Modularity Of Twisted Index In CHL Models