TY - JOUR

T1 - Twisted Elliptic Genus for K3 and Borcherds Product

AU - Eguchi, Tohru

AU - Hikami, Kazuhiro

N1 - Funding Information:
T.E. would like thank California Institute for Technology and Professors H. Oog-uri and J.H. Schwarz for Moore distinguished scholarship during the fall of 2011 and kind hospitality. K.H. thanks the Simons Center for Geometry and Physics for hospitality in the summer of 2011. The authors would like to thank H. Aoki for sending them an unpublished manuscript. Thanks are also to M. Kaneko for communications. This work is supported in part by Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

PY - 2012/11

Y1 - 2012/11

N2 - We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M 24. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M 24, can be represented in a very simple manner in terms of the η 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.

AB - We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M 24. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M 24, can be represented in a very simple manner in terms of the η 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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U2 - 10.1007/s11005-012-0569-2

DO - 10.1007/s11005-012-0569-2

M3 - Article

AN - SCOPUS:84867714038

SN - 0377-9017

VL - 102

SP - 203

EP - 222

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2

ER -