自由Bosonic格顶点算子代数的亏格两分拆函数
The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras
摘要：
我们定义了亏格为2的黎曼曲面上的顶点算子代数的$n$ -点函数，在两个不同的缝合方案中，要么两个环面缝合在一起，要么一个环面上缝合一个手柄.在这两种缝纫方案中，我们明确地得到了Heisenberg自由玻色弦和格顶点算子代数的亏格两个分拆函数的闭公式。我们证明了在给定的适当区域上，分拆函数在缝纫参数下是全纯的，并描述了它们的模性质。最后，我们表明，分拆函数不能是相等的两个环面退化点，他们可以明确地比较附近。
英文摘要：
We define the $n$-point function for a vertex operator algebra on a genus two Riemann surface in two separate sewing schemes where either two tori are sewn together or a handle is sewn to one torus. We explicitly obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and lattice vertex operator algebras in both sewing schemes. We prove that the partition functions are holomorphic in the sewing parameters on given suitable domains and describe their modular properties. Finally, we show that the partition functions cannot be equal in the neighborhood of a two-tori degeneration point where they can be explicitly compared.
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