v 1 5 O ct 1 99 4 DAMTP 94 - 80 CONFORMAL FIELD
نویسندگان
چکیده
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(Λ) and˜H(Λ) respectively , which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct lattices Λ C and˜Λ 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(Λ) and˜H(Λ) are self-dual if and only if Λ is. We show that H(Λ C) has a natural " triality " structure, which induces an isomorphism H(˜ Λ C) ≡ ˜ H(Λ C) and also a triality structure oñ H(˜ Λ C). For C the Golay code, ˜ Λ C is the Leech lattice, and the triality oñ H(˜ Λ 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(Λ) and˜H(Λ) 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.
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تاریخ انتشار 1996