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arXiv · 1711.09698

Calabi-Yau manifolds and sporadic groups

Andreas Banlaki·Abhishek Chowdhury·Abhiram Kidambi·Maria Schimpf·Harald Skarke·Timm Wrase
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Abstract

A few years ago a connection between the elliptic genus of the K3 manifold and the largest Mathieu group M$_{24}$ was proposed. We study the elliptic genera for Calabi-Yau manifolds of larger dimensions and discuss potential connections between the expansion coefficients of these elliptic genera and sporadic groups. While the Calabi-Yau 3-fold case is rather uninteresting, the elliptic genera of certain Calabi-Yau $d$-folds for $d>3$ have expansions that could potentially arise from underlying sporadic symmetry groups. We explore such potential connections by calculating twined elliptic genera for a large number of Calabi-Yau 5-folds that are hypersurfaces in weighted projected spaces, for a toroidal orbifold and two Gepner models.

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Andreas Banlaki, Abhishek Chowdhury, Abhiram Kidambi, Maria Schimpf, Harald Skarke, Timm Wrase. 2017-11-27. Calabi-Yau manifolds and sporadic groups. https://doi.org/10.1007/jhep02(2018)129

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