Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-03-04
Physics
High Energy Physics
High Energy Physics - Theory
28+1 pages, no figure, Contribution to the Proceedings of the workshop in honour of Professor Tsuchiya's retirement, Nagoya Un
Scientific paper
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 ${\cal N}=4$ superconformal algebra.
Eguchi Tohru
Sugawara Yuji
Taormina Anne
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