Discussion of Self-Dual c=24 Conformal Field Theories

TL;DR

This paper explores the classification and construction of self-dual c=24 conformal field theories, focusing on the uniqueness of the Monster module and proposing new theories through orbifold techniques.

Contribution

It introduces new methods for constructing self-dual c=24 conformal field theories and provides evidence for the existence of theories beyond previously known classifications.

Findings

Evidence for several new conformal field theories

Analysis of orbifold constructions and their role in theory classification

Discussion on the uniqueness of the Monster module V^ atural

Abstract

We discuss questions arising from the recent work of Schellekens, and also from an earlier paper by Schellekens and Yankielowicz. We summarise Schellekens' results, and proceed to discuss the uniqueness of the c=24 self-dual conformal field theory with no weight one states, i.e. the Monster module $V^\natural$. After introducing the concept of complementary representations, we examine $Z_2$-orbifold constructions in general, and then proceed to apply our considerations firstly to the specific case of the FKS constructions $H(\Lambda)$ and then to the reflection twisted theories $\widetilde H(\Lambda)$. Our techniques provide evidence for the existence of several new theories beyond those proven to exist in previous work and conjectured to exist in Schellekens and Yankielowicz.