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Seminario: MARTES 15 DE SETIEMBRE 15 HS.

AULA DEL IAFE

"On fusion graphs for Lie groups at level k"

Robert Coquereaux
Centre de Physique Théorique (Marseille)

Abstract:

Primary fields of rational conformal field theories, in particular WZW
models associated with a Lie group G at level k (a non negative
integer), obey fusion rules that can be encoded by graphs.
This is also true for conformal boundary states in the framework of
boundary CFT.
When G is SU(2), those ``fusion graphs'' coincide with the ADE simply
laced Dynkin diagrams: this is essentially the result of a
classification that was obtained in 1987.
Classifications are now available for other Lie groups: SU(3)
(obtained in 1992) and  SU(4) (obtained in 2000), but a solution to   the
general classification problem remains to be found.
Mathematically, the problem amounts to study the modular categories
associated with pairs (G,k) and to determine their associated module-
categories.
In this talk, after summarizing the known classifications,  we shall
present  fusion graphs attached to diagonal theories associated with
arbitrary simple Lie groups (including exceptional ones), for
relatively small values of the level, and discuss properties of
different types of graphs attached to non-diagonal theories.
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