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Liouville field, Modular forms, Elliptic genera.

Eguchi, T. and Sugawara, Y. and Taormina, A. (2007) 'Liouville field, Modular forms, Elliptic genera.', Journal of high energy physics., 03 . p. 119.


When we describe 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. Consistency of our approach is assured by some remarkable identity of theta functions whose proof, by D. Zagier, is included in an appendix.

Item Type:Article
Keywords:Conformal field theory, String theory.
Full text:PDF - Accepted Version (321Kb)
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Publisher statement:© 2007 IOP Publishing
Record Created:25 Apr 2007
Last Modified:05 Nov 2014 10:24

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