Classification of Ten-Dimensional Heterotic Strings

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.

14 pages

Cited by in corpus (14)

• Meromorphic c=24 Conformal Field Theories
• WZW Commutants, Lattices, and Level 1 Partition Functions
• Orbifold Constructions and the Classification of Self-Dual c=24 Conformal Field Theories
• Partition Functions for Heterotic WZW Conformal Field Theories
• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices
• Discussion of Self-Dual c=24 Conformal Field Theories
• On the Uniqueness of the Twisted Representation in the Z_2 Orbifold Construction of a Conformal Field Theory from a Lattice
• Transformations among large c conformal field theories
• On the duality of F-theory and the CHL string in seven dimensions
• Intertwiners in Orbifold Conformal Field Theories
• Fermion Currents on Asymmetric Orbifolds
• Continuous Symmetries of Lattice Conformal Field Theories and their $Z_2$-Orbifolds
• On Representations of Conformal Field Theories and the Construction of Orbifolds
• On the classification of (2,1) heterotic strings