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

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

1994-03-16

arxiv.org/abs/hep-th/9403088v1

Nucl.Phys. B428 (1994) 233-258

Physics

High Energy Physics

High Energy Physics - Theory

31 pages

Scientific paper

10.1016/0550-3213(94)90201-1

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 $\widetilde H(\Lambda)$, 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 $\widetilde H(\Lambda)$, and of meromorphic theories in general, introducing the concept of deterministic theories.

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