Liouville Field, Modular Forms and Elliptic Genera

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1579226