Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24
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DOI：
10.1112/plms/pdr041
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发表时间：
2010-10
影响因子：
1.8
通讯作者：
C. Lam;Hiroki Shimakura
中科院分区：
文献类型：
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作者：
C. Lam;Hiroki Shimakura
1993年，Schellekens发表了《亚纯c=24共形场理论》，《通信数学物理》153（1993）159-185。得到了71个可能的具有中心荷24的全纯顶点算子代数的李代数的列表。然而，并不是所有的案件都已知存在。利用框架顶点算子代数理论构造了一类新的全纯顶点算子代数，并确定了它们的权1子空间的李代数结构。特别地，我们研究了与长度为48的三重偶码RM（1，4）3和RM（1，4）n（d16+）的子码相关的全纯框架顶点算子代数。𝒟这些VOA对应于晶格类型VOA（V2 E8+）<$3和V2 E8 +<$V2D16 ++的全纯简单电流扩展。当W=（V2 E8+）<$3或V2 E8 +<$V2D16 ++时，我们利用W的所有不可约模R（W）的集合上的二次空间结构来确定这样的扩张。作为我们的主要结果，我们构造了Schellekens列表中的七个新的中心电荷为24的全纯框架VOA，并得到了与中心电荷为24的全纯框架VOA的权1子空间相关联的所有李代数结构的完整列表。
In 1993, Schellekens [‘Meromorphic c=24 conformal field theories’, Comm. Math. Phys. 153 (1993) 159–185.] obtained a list of possible 71 Lie algebras of holomorphic vertex operator algebras with central charge 24. However, not all cases are known to exist. The aim of this article is to construct new holomorphic vertex operator algebras (VOAs) using the theory of framed VOAs and to determine the Lie algebra structures of their weight 1 subspaces. In particular, we study holomorphic framed vertex operator algebras associated to subcodes of the triply even codes RM(1, 4)3 and RM(1, 4)⊕ 𝒟(d16+) of length 48. These VOAs correspond to the holomorphic simple current extensions of the lattice type VOAs (V2E8+)⊗3 and V2E8+⊗V2D16++ . We determine such extensions using a quadratic space structure on the set of all irreducible modules R(W) of W when W=(V2E8+)⊗3 or V2E8+⊗V2D16++ As our main results, we construct seven new holomorphic VOAs of central charge 24 in Schellekens' list and obtain a complete list of all Lie algebra structures associated to the weight 1 subspaces of holomorphic framed VOAs of central charge 24.