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Liouville field, modular forms and elliptic genera.

Eguchi, T. and Sugawara, Y. and Taormina, A. (2007) 'Liouville field, modular forms and elliptic genera.', Journal of high energy physics., 2007 (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:(AM) Accepted Manuscript
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Publisher statement:© SISSA 2007. Published by IOP Publishing for SISSA. This is an author-created, un-copyedited version of an article accepted for publication in Journal of high energy physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1126-6708/2007/03/119.
Date accepted:19 March 2007
Date deposited:16 April 2013
Date of first online publication:March 2007
Date first made open access:No date available

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