Talk page
Title:
Modular invariant partition functions return from the dead
Speaker:
Abstract:
Modular invariant torus partition functions are the simplest quantity associated with the full (as opposed to chiral) rational conformal field theory. In 1986, Cappelli-Itzykson-Zuber classified these for the theories with chiral algebra coming from sl(2), and found they fall into an A-D-E pattern: they are the Wess- Zumino-Witten models associated to SU(2) (these form the `A'), to SO(3) (these are the `D'), along with 3 exceptionals (these are the `E'). In the 1990s Galois methods were introduced, and the sl(3) classification was done and related to Jacobians of Fermat curves. At the turn of the century subfactor people, led by Ocneanu, introduced new techniques, notably alpha-induction. In my talk I'll explain how combining the old and the new allows for classifications to be completed for all Lie algebras of rank up to 8 or so.
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