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

Abstract

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 ($\le 4$). 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.

arXiv comment18pp [Talk given by one of us (F.R.) at the ``Research Conference on Advanced Quantum Field Theory and Critical Phenomena'', Como (Italy), June 17-21, 1991]

Cited by in corpus (8)

• Fusion rules in conformal field theory
• On the Classification of Modular Fusion Algebras
• On the classification of fusion rings
• Fusion Algebras of Fermionic Rational Conformal Field Theories via a Generalized Verlinde Formula
• Fusion potentials I
• Virasoro Representations on Fusion Graphs
• Polynomial rings of the chiral $SU(N{)}_2$ models
• On fusion algebra of chiral $SU(N{)}_k$ models