Calabi-Yau manifolds and sporadic groups

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.

arXiv comment34 pages;v2 minor corrections

References in corpus (23)

• Notes on the K3 Surface and the Mathieu group M_24
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• On the Landau-Ginzburg Description of $N=2$ Minimal Models
• Note on Twisted Elliptic Genus of K3 Surface
• Mathieu twining characters for K3
• No Mirror Symmetry in Landau-Ginzburg Spectra!
• Mathieu Moonshine in the elliptic genus of K3
• BKM Lie superalgebras from dyon spectra in Z_N-CHL orbifolds for composite N
• BKM Lie superalgebras from counting twisted CHL dyons
• Symmetry-surfing the moduli space of Kummer K3s
• Mathieu Moonshine and N=2 String Compactifications
• The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_24
• PALP - a User Manual
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Twining Genera of (0,4) Supersymmetric Sigma Models on K3
• Heterotic string on the CHL orbifold of K3
• The Hodge-elliptic genus, spinning BPS states, and black holes
• N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds
• $\mathcal{N}=2$ heterotic string compactifications on orbifolds of $K3\times T^2$
• Mathieu moonshine in four dimensional $\mathcal{N}=1$ theories
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds
• N=2 Moonshine

Cited by in corpus (2)

• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• On Mathieu moonshine and Gromov-Witten invariants