2008/03/04 by Tohru Eguchi, Eguchi, Tohru, Yuji Sugawara +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.48550/arxiv.0803.0377
28+1 pages, no figure, Contribution to the Proceedings of the workshop in honour of Professor Tsuchiya's retirement, Nagoya University, March 2007
arxiv created 2008/03/04 · openalex publication_date 2008/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.