On conformal field theories with low number of primary fields

Abstract

Using Verlinde formula and the symmetry of the modular matrix we describe an algorithm to find all conformal field theories with low number of primary fields. We employ the algorithm on up to eight primary fields. Four new conformal field theories are found which do not appear to come from current algebras. This supports evidence to the fact that rational conformal field theories are far richer than suspected before.

arXiv comment16 pages. Deleted two $SO(3{)}_{4r}$ conformal data and added one new one

References in corpus (4)

• On the classification of fusion rings
• Foundations of Rational Quantum Field Theory, I
• Galois Groups in Rational Conformal Field Theory
• Galois groups in rational conformal field theory II. The discriminant

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