Liouville Field, Modular Forms and Elliptic Genera

Eguchi, T.; Sugawara, Y.; Taormina, A.

doi:10.1088/1126-6708/2007/03/119

Liouville Field, Modular Forms and Elliptic Genera

Eguchi, T.; Sugawara, Y.; Taormina, A.

Authors

T. Eguchi

Y. Sugawara

Professor Anne Taormina anne.taormina@durham.ac.uk
Professor

Abstract

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.

Citation

Eguchi, T., Sugawara, Y., & Taormina, A. (2007). Liouville Field, Modular Forms and Elliptic Genera. Journal of High Energy Physics, 2007(03), https://doi.org/10.1088/1126-6708/2007/03/119

Journal Article Type	Article
Acceptance Date	Mar 19, 2007
Publication Date	Mar 29, 2007
Deposit Date	Apr 25, 2007
Publicly Available Date	Apr 16, 2013
Journal	Journal of High Energy Physics
Print ISSN	1126-6708
Electronic ISSN	1029-8479
Publisher	Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed	Peer Reviewed
Volume	2007
Issue	03
DOI	https://doi.org/10.1088/1126-6708/2007/03/119
Keywords	Conformal field theory, String theory.

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Copyright 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.