Generalized Kac-Moody Algebras from CHL dyons

Abstract

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.

LaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references added

References in corpus (23)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Algebras, BPS States, and Strings
• Duality Symmetric Actions
• Counting Dyons in N=4 String Theory
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Exact Counting of Black Hole Microstates
• Four Dimensional String/String/String Triality
• Maximally Supersymmetric String Theories in D<10
• Precision Counting of Small Black Holes
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Entropy Function for Heterotic Black Holes
• On the algebras of BPS states
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Dyon Spectrum in CHL Models
• Exact and Asymptotic Degeneracies of Small Black Holes
• Product Representation of Dyon Partition Function in CHL Models
• The Igusa modular forms and ``the simplest'' Lorentzian Kac--Moody algebras
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Black Holes, Elementary Strings and Holomorphic Anomaly
• Spectrum of CHL Dyons from Genus-Two Partition Function
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• Rare Decay Modes of Quarter BPS Dyons
• Dyon Death Eaters

Cited by in corpus (20)

• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• Supersymmetric Index from Black Hole Entropy
• M-strings, Elliptic Genera and N=4 String Amplitudes
• BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Black Hole Microstate Counting and its Macroscopic Counterpart
• BKM Lie superalgebras from counting twisted CHL 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
• Unravelling Mathieu Moonshine
• 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
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Borcherds Algebras and N=4 Topological Amplitudes
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• Twisted elliptic genus for K3 and Borcherds product
• Mathieu Moonshine and Siegel Modular Forms