Orbifold Constructions and the Classification of Self-Dual c=24 Conformal Field Theories

Abstract

We discuss questions arising from the work of Schellekens. After introducing the concept of complementary representations, we examine $Z_2$-orbifold constructions in general, and propose a technique for identifying the orbifold theory without knowledge of its explicit construction. This technique is then generalised to twists of order 3, 5 and 7, and we proceed to apply our considerations to the FKS constructions $H(\Lambda )$ ($\Lambda$ an even self-dual lattice) and the reflection-twisted orbifold theories $\tilde{H}(\Lambda )$, which together remain the only $c=24$ theories which have so far been proven to exist. We also make, in the course of our arguments, some comments on the automorphism groups of the theories $H(\Lambda )$ and $\tilde{H}(\Lambda )$, and of meromorphic theories in general, introducing the concept of deterministic theories.

31 pages

References in corpus (4)

• Meromorphic c=24 Conformal Field Theories
• Conformal Field Theories, Representations and Lattice Constructions
• Classification of Ten-Dimensional Heterotic Strings
• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices

Cited by in corpus (17)

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• Monstrous String-String Duality
• Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms
• Cosets of Meromorphic CFTs and Modular Differential Equations
• Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras
• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices
• Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras
• An Extremal N=2 Superconformal Field Theory
• Extremal chiral $\mathcal{N}=4$ SCFT with $c=24$
• 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
• A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24
• Continuous Symmetries of Lattice Conformal Field Theories and their $Z_2$-Orbifolds
• On the classification of (2,1) heterotic strings