# BKM Lie superalgebras from counting twisted CHL dyons -- II

## TL;DR

This paper expands the classification of Borcherds-Kac-Moody Lie superalgebras linked to quarter-BPS dyons in string theory by incorporating connections with moonshine phenomena and proposing new algebraic structures from dyon generating functions.

## Contribution

It introduces new BKM Lie superalgebras associated with $ ext{Z}_5$ and $ ext{Z}_6$ CHL orbifolds using moonshine connections and demonstrates modularity properties of related Siegel modular forms.

## Key findings

- New BKM Lie superalgebras from $ ext{Z}_5$ and $ ext{Z}_6$ orbifolds
- Modularity of Siegel modular forms in moonshine contexts
- Connections established between dyon counting functions and moonshine phenomena

## 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.