On conformal field theories with low number of primary fields

TL;DR

This paper introduces an algorithm based on the Verlinde formula and modular symmetry to classify low-primary-field conformal field theories, discovering four new theories beyond current algebra origins, indicating greater richness in rational CFTs.

Contribution

The authors develop a novel algorithm for classifying low-primary-field conformal field theories and identify four new theories not derived from current algebras.

Findings

Four new conformal field theories discovered

Algorithm successfully applied to up to eight primary fields

Evidence suggests rational CFTs are more diverse than previously thought

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.