BKM Lie superalgebras from counting twisted CHL dyons -- II

Abstract

We revisit our earlier work which lead to a periodic table of Borcherds-Kac-Moody algebras that appeared in the context of the refined generating function of quarter-BPS (dyons) in $\mathcal{N}=4$ supersymmetric four-dimensional string theory. We make new additions to the periodic table by making use of connections with generalized Mathieu moonshine as well as umbral moonshine. We show the modularity of some Siegel modular forms that appear in umbral moonshine associated with Niemeier lattices constructed from A-type root systems and further show that the same Siegel modular forms appear for generalized Mathieu moonshine in some cases. We argue for the existence of a new kind of BKM Lie superalgebras that arise from the dyon generating functions for the ${\mathbb{Z}}_5$ and ${\mathbb{Z}}_6$ CHL orbifolds.

arXiv comment36 pages; (v2) 39 pages, Matches published version and presentation has been improved

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Cited by in corpus (15)

• Fricke S-duality in CHL models
• How Do Black Holes Predict the Sign of the Fourier Coefficients of Siegel Modular Forms?
• Unravelling Mathieu Moonshine
• Brewing moonshine for Mathieu
• Mathieu Moonshine and Orbifold K3s
• Second Quantized Mathieu Moonshine
• BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• Symmetries of K3 sigma models
• Positivity of discrete information for CHL black holes
• Two moonshines for $L_2(11)$ but none for $M_{12}$
• Mathieu Moonshine and Siegel Modular Forms
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras
• A study on free roots of Borcherds-Kac-Moody Lie Superalgebras
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras -- II