Comments on M${}_{24}$ representations and $C{Y}_3$ geometries

Abstract

We show using string dualities that Mathieu moonshine controls Gromov-Witten invariants and periods of the holomorphic 3-form $\Omega$ for certain $C{Y}_3$ manifolds. We also discuss how the period vectors appear in flux compactifications on these $C{Y}_3$ manifolds and work out the connection between the sporadic group M${}_{24}$ and the Yukawa couplings in four dimensional theories that arise from heterotic string theory compactifications on these $C{Y}_3$ manifolds.

arXiv comment27 pages, v2: minor additions, published version

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Cited by in corpus (3)

• On Mathieu moonshine and Gromov-Witten invariants
• On the elliptic genera of manifolds of Spin(7) holonomy
• Calabi-Yau manifolds and sporadic groups