Twisted elliptic genus for K3 and Borcherds product

Abstract

We further discuss the relation between the elliptic genus of K3 surface and the Mathieu group M24. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M24, can be represented in a very simple manner in terms of the eta-product of the corresponding conjugacy classes. It is shown that our formula is a consequence of the identity between the Borcherds product and additive lift of some Siegel modular forms.

17 pages

References in corpus (8)

• Notes on the K3 Surface and the Mathieu group M_24
• Note on Twisted Elliptic Genus of K3 Surface
• Mathieu twining characters for K3
• Product Representation of Dyon Partition Function in CHL Models
• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
• Mathieu Moonshine in the elliptic genus of K3
• Generalized Kac-Moody Algebras from CHL dyons
• Superconformal Algebras and Mock Theta Functions

Cited by in corpus (5)

• Eisenstein series and automorphic representations
• Fricke S-duality in CHL models
• A K3 sigma model with Z_2^8:M_{20} symmetry
• On symmetries of N=(4,4) sigma models on T^4
• Mathieu Moonshine and Siegel Modular Forms