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VOL. 61 | 2011 Modular forms and elliptic genera for ALE spaces
Tohru Eguchi, Yuji Sugawara, Anne Taormina

Editor(s) Koji Hasegawa, Takahiro Hayashi, Shinobu Hosono, Yasuhiko Yamada


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. Consistency of our approach is assured by some remarkable identity of theta functions.

We include in the appendix some new materials on the representation theory of $\mathcal{N} = 4$ superconformal algebra.


Published: 1 January 2011
First available in Project Euclid: 24 November 2018

zbMATH: 1243.81188
MathSciNet: MR2867146

Digital Object Identifier: 10.2969/aspm/06110125

Rights: Copyright © 2011 Mathematical Society of Japan


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