Meromorphic c=24 Conformal Field Theories

TL;DR

This paper classifies all possible meromorphic conformal field theories with central charge 24 and a single primary field, suggesting the existence of 71 such theories, expanding on known models.

Contribution

It systematically enumerates all meromorphic c=24 theories with specific Kac-Moody algebra combinations, revealing new potential theories beyond known examples.

Findings

Identified 71 meromorphic c=24 theories, including 30 new ones.

Confirmed the structure of theories with spin-1 currents and their algebraic compositions.

Extended the classification of c=24 conformal field theories with modular invariance.

Abstract

Modular invariant conformal field theories with just one primary field and central charge $c=24$ are considered. It has been shown previously that if the chiral algebra of such a theory contains spin-1 currents, it is either the Leech lattice CFT, or it contains a Kac-Moody sub-algebra with total central charge 24. In this paper all meromorphic modular invariant combinations of the allowed Kac-Moody combinations are obtained. The result suggests the existence of 71 meromorphic $c=24$ theories, including the 41 that were already known.