BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N

Abstract

We show that the generating function of electrically charged 1/2-BPS states in N=4 supersymmetric Z_N-CHL orbifolds of the heterotic string on T^6 are given by multiplicative eta-products. The eta-products are determined by the cycle shape of the corresponding symplectic involution in the dual type II picture. This enables us to complete the construction of the genus-two Siegel modular forms due to David, Jatkar and Sen [arXiv:hep-th/0609109] for Z_N orbifolds when N is non-prime. We study the Z_4 CHL orbifold in detail and show that the associated Siegel modular forms, Φ_3(Z) and \widetildeΦ_3(Z), are given by the square of the product of three even genus-two theta constants. Extending work by us[arXiv:0807.4451] as well as Cheng and Dabholkar[arXiv:0809.4258], we show that their `square roots' appear as the denominator formulae of two distinct Borcherds-Kac-Moody (BKM) Lie superalgebras. The BKM Lie superalgebra associated with the generating function of 1/4-BPS states, i.e., \widetildeΦ_3(Z) has a parabolic root system with a light-like Weyl vector and the walls of its fundamental Weyl chamber are mapped to the walls of marginal stability of the 1/4-BPS states.

LaTeX, 44 pages, 2 figures (v2)Physical interpretation for a family of BKM Lie superalgebras provided; typos corrected

References in corpus (13)

• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
• Comments on the Spectrum of CHL Dyons
• Product Representation of Dyon Partition Function in CHL Models
• Dyon Spectrum in N=4 Supersymmetric Type II String Theories
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Duality Orbits, Dyon Spectrum and Gauge Theory Limit of Heterotic String Theory on T^6
• U-duality Invariant Dyon Spectrum in type II on T^6
• S-duality Action on Discrete T-duality Invariants
• Generalized Kac-Moody Algebras from CHL dyons
• Kinematical Analogy for Marginal Dyon Decay
• BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications

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