Moonshine: The First Quarter Century and Beyond: Modularity of Trace Functions in Orbifold Theory for ℤ-Graded Vertex Operator Superalgebras
Moonshine: The First Quarter Century and Beyond: Modularity of Trace Functions in Orbifold Theory for ℤ-Graded Vertex Operator Superalgebras
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DOI：
10.1017/cbo9780511730054.007
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发表时间：
2006-01
期刊：
影响因子：
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通讯作者：
C. Dong;Zhongping Zhao
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文献类型：
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作者：
C. Dong;Zhongping Zhao
研究了Z-分次顶点算子超代数Orbiford理论中的迹函数，得到了一个模不变性结果。更精确地说，设V是一个C_2-余有限Z-分次顶点算子超代数，G是V的有限自同构群，则对G中的任意交换对（g，h），与简单g-扭V-模相关联的h\sigma-迹函数在上半平面上是全纯的，其中\sigma是V上来自V的超空间结构的标准对合。迹函数给出了满模群SL（2，Z）的一个表示.
We study the trace functions in orbiford theory for Z-graded vertex operator superalgebras and obtain a modular invariance result. More precisely, let V be a C_2-cofinite Z-graded vertex operator superalgebra and G a finite automorphism group of V. Then for any commuting pairs (g,h) in G, the h\sigma-trace functions associated to the simple g-twisted V-modules are holomorphic in the upper half plane where \sigma is the canonical involution on V coming from the superspace structure of V. If V is further g-rational for every g n G, the trace unctions afford a representation for the full modular group SL(2,Z).