TOWARDS A CLASSIFICATION OF FUSION RULE ALGEBRAS IN RATIONAL CONFORMAL FIELD THEORIES

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 (≤4). We then turn our attention to FRA’s generated polynomially by...

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Published inInternational journal of modern physics. B, Condensed matter physics, statistical physics, applied physics Vol. 6; no. 11n12; pp. 2075 - 2090
Main Authors CASELLE, M., PONZANO, G., RAVANINI, F.
Format Journal Article
LanguageEnglish
Published United States World Scientific Publishing Company 01.06.1992
Subjects
661100 > Classical & Quantum Mechanics > (1992-)
ALGEBRA
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CLASSIFICATION
CONFORMAL INVARIANCE
DOCUMENT TYPES
FIELD THEORIES
FUNCTIONS
II. QUANTUM FIELD THEORY MODELS: Conformal Field Theory Statistical Mechanic Models and Quantum Field Theory
INVARIANCE PRINCIPLES
MATHEMATICS 662110 > General Theory of Particles & Fields > Theory of Fields & Strings > (1992-)
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POLYNOMIALS
REVIEWS
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ISSN0217-9792
1793-6578
DOI10.1142/S021797929200102X

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Summary: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 (≤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.
Bibliography:None
ISSN:0217-9792
1793-6578
DOI:10.1142/S021797929200102X