Exceptional Vertex Operator Algebras and the Virasoro Algebra
Exceptional Vertex Operator Algebras and the Virasoro Algebra
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卓越的顶点算子代数和 Virasoro 代数
DOI：
10.1090/conm/497/09780
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Tuite
中科院分区：
文献类型：
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作者：
M. Tuite
我们考虑特殊顶点算子代数，特别是卡西米尔向量构造的最低共形权的主要向量Virasoro后裔的真空。我们讨论这些理论的限制，从适当的属零和属一个两点相关函数的分析。我们发现明确的微分方程的配分函数的情况下，最低的重量主要向量形成一个李代数或格里斯代数。例子包括Wess-Zumino-维滕模型的德利涅的例外李代数和月光模块。我们部分验证了Deligne例外李代数张量积的不可约分解，并考虑了Griess代数张量积的类似分解的可能性。本文简要地讨论了维滕最近关于三维黑洞的工作中所产生的一些有约束的极值顶点算子代数。
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that follow from an analysis of appropriate genus zero and genus one two point correlation functions. We find explicit differential equations for the partition function in the cases where the lowest weight primary vectors form a Lie algebra or a Griess algebra. Examples include the Wess-Zumino-Witten model for Deligne's exceptional Lie algebras and the Moonshine Module. We partially verify the irreducible decomposition of the tensor product of Deligne's exceptional Lie algebras and consider the possibility of similar decompositions for tensor products of the Griess algebra. We briefly discuss some conjectured extremal vertex operator algebras arising in Witten's recent work on three dimensional black holes.