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The Cappelli-Itzykson-Zuber A-D-E classification

T. Gannon
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Abstract

In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine $A_1$ 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.

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T. Gannon. 1999-02-18. The Cappelli-Itzykson-Zuber A-D-E classification. https://doi.org/10.1142/s0129055x00000265

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