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arXiv · 2207.10502

$\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras -- II

Suresh Govindarajan·Mohammad Shabbir
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Abstract

The square-root of Siegel modular forms of CHL Z_N orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for N=1,2,3,4. We study the decomposition of these Siegel modular forms in terms of characters of two sub-algebras: one is a $\widehat{sl(2)}$ and the second is a Borcherds extension of the $\widehat{sl(2)}$. This is a continuation of our previous work where we studied the case of Siegel modular forms appearing in the context of Umbral moonshine. This situation is more intricate and provides us with a new example (for N=5) that did not appear in that case. We restrict our analysis to the first N terms in the expansion as a first attempt at deconstructing the Siegel modular forms and unravelling the structure of potentially new Lie algebras that occur for N=5,6.

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Suresh Govindarajan, Mohammad Shabbir. 2022-07-21. $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras -- II. https://doi.org/10.1016/j.nuclphysb.2023.116127

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