The Cappelli-Itzykson-Zuber A-D-E classification
Abstract
In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed -- in hindsight the reason is that their argument ignored most of the rich mathematical structure present. We give here the "modern" proof of their result; it is an order of magnitude simpler and shorter, and much of it has already been extended to all other affine algebras. We conclude with some remarks on the A-D-E pattern appearing in this and other RCFT classifications.
Cite
@article{arxiv.math/9902064,
title = {The Cappelli-Itzykson-Zuber A-D-E classification},
author = {T. Gannon},
journal= {arXiv preprint arXiv:math/9902064},
year = {2009}
}
Comments
10 pages, plain tex; an historical remark on A-D-E corrected, 2 references added, several new comments added to conclusion