关于四穿孔球面的单值问题
On the monodromy problem for the four-punctured sphere
摘要：
我们考虑了四穿孔球的单值问题，其中一个复合单值的性质是固定的，通过直接看模$x$中的辅助参数的展开，而不考虑无限中心荷的量子共形块的限制.积分出现在展开的Volterra方程，涉及产品的两个超几何函数的一阶和多达四个超几何函数的二阶。它表明，所有这样的积分可以计算解析。给出了模中一阶和二阶辅助参数的完整解析计算。结果与假设无限中心荷极限下量子共形块的指数假设所得到的评价一致。扩展到更高的订单进行了讨论。
英文摘要：
We consider the monodromy problem for the four-punctured sphere in which the character of one composite monodromy is fixed, by looking at the expansion of the accessory parameter in the modulus $x$ directly, without taking the limit of the quantum conformal blocks for infinite central charge. The integrals which appear in the expansion of the Volterra equation, involve products of two hypergeometric functions to first order and up to four hypergeometric functions to second order. It is shown that all such integrals can be computed analytically. We give the complete analytical evaluation of the accessory parameter to first and second order in the modulus. The results agree with the evaluation obtained by assuming the exponentiation hypothesis of the quantum conformal blocks in the limit of infinite central charge. Extension to higher orders is discussed.
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