Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-10-05
Commun.Math.Phys.179:61-120,1996
Physics
High Energy Physics
High Energy Physics - Theory
65 pages
Scientific paper
10.1007/BF02103716
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.
Dolan Louise
Goddard Peter
Montague P.
No associations
LandOfFree
Conformal Field Theories, Representations and Lattice Constructions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Conformal Field Theories, Representations and Lattice Constructions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conformal Field Theories, Representations and Lattice Constructions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-262020