Twisted elliptic genus for K3 and Borcherds product

Details Twisted elliptic genus for K3 and Borcherds product Twisted elliptic genus for K3 and Borcherds product

2011-12-27

arxiv.org/abs/1112.5928v1

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

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.

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