Towards a Classification of Fusion Rule Algebras in Rational Conformal Field Theories

Details Towards a Classification of Fusion Rule Algebras in Rational Conformal Field Theories Towards a Classification of Fusion Rule Algebras in Rational Conformal Field Theories

1991-11-15

arxiv.org/abs/hep-th/9111027v1

Int.J.Mod.Phys.B6:2075-2090,1992

Physics

High Energy Physics

High Energy Physics - Theory

18pp [Talk given by one of us (F.R.) at the ``Research Conference on Advanced Quantum Field Theory and Critical Phenomena'', C

Scientific paper

10.1142/S021797929200102X

We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq 4$). We then turn our attention to FRA's generated polynomially by one (real) fundamental field, for which a classification is known. Attempting to generalize this result, we describe some connections between FRA's and Graph Theory. The possibility to get new results on the subject following this ``graph'' approach is briefly discussed.

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