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.

27 pages, v2: minor additions, published version

References in corpus (7)

• Flux Compactification
• Notes on the K3 Surface and the Mathieu group M_24
• Note on Twisted Elliptic Genus of K3 Surface
• Mathieu Moonshine in the elliptic genus of K3
• D-Terms from Generalized NS-NS Fluxes in Type II
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• Mirror Symmetry for Toric Branes on Compact Hypersurfaces

Cited by in corpus (1)

• On the elliptic genera of manifolds of Spin(7) holonomy