Classification of Ten-Dimensional Heterotic Strings

TL;DR

This paper advances the classification of ten-dimensional heterotic strings by analyzing meromorphic conformal field theories with central charge 24, identifying possible algebraic structures and suggesting the existence of new theories.

Contribution

It provides a complete list of all ten-dimensional heterotic strings and proposes a framework for classifying meromorphic c=24 theories based on Kac-Moody algebra combinations.

Findings

Complete list of ten-dimensional heterotic strings.

221 possible Kac-Moody algebra combinations.

Evidence for at least 20 new meromorphic c=24 theories.

Abstract

Progress towards the classification of the meromorphic $c=24$ conformal field theories is reported. It is shown if such a theory has any spin-1 currents, it is either the Leech lattice CFT, or it can be written as a tensor product of Kac-Moody algebras with total central charge 24. The total number of combinations of Kac-Moody algebras for which meromorphic $c=24$ theories may exist is 221. The next step towards classification is to obtain all modular invariant combinations of Kac-Moody characters. The presently available results are sufficient to obtain a complete list of all ten-dimensional heterotic strings. Furthermore there are strong indications for the existence of several (probably at least 20) new meromorphic $c=24$ theories.