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Modular Forms and Elliptic Genera for ALE Spaces · Around

2008

Modular Forms and Elliptic Genera for ALE Spaces

Eguchi, Tohru, Sugawara, Yuji, Taormina, Anne

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When we describe string propagation on non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory.

These representations mix in an intricate way under the modular transformations.
In this article, we propose a method of combining discrete and continuous representations so that the resulting combinations have a simpler modular behavior and can be used as conformal blocks of the theory.
We compute elliptic genera of ALE spaces and obtain results which agree with those suggested from the decompactification of K3 surface.

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2002

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2004

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V. Fateev, A. B. Zamolodchikov and A. B. Zamolodchikov, arXiv:hep-th/0001012; J. Teschner, arXiv:hep-th/0009138; A. B. Zamolodchikov and A. B. Zamolodchikov, arXiv:hep-th/0101152;

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W. Lerche, arXiv:hep-th/0006100

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A. Polishchuk, arXiv:math.AG/9810084

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T. Eguchi, Y. Sugawara and A. Taormina, ”Liouville Field, Modular Forms and Elliptic Genera”, JHEP 0703

2007

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