We extend the modular orbits method of constructing a two-dimensional orbifold conformal field theory to higher genus Riemann surfaces. We find that partition functions on surfaces of arbitrary genus can be constructed by a straightforward generalization of the rules that one would apply to the torus. We demonstrate how one can use these higher genus objects to compute correlation functions and OPE coefficients in the underlying theory. In the case of orbifolds of free bosonic theories by subgroups of continuous symmetries, we can give the explicit results of our procedure for symmetric and asymmetric orbifolds by cyclic groups.

中文翻译：

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较高属的模块化轨道

我们将构建二维轨道共形共形场理论的模轨道方法扩展到更高的黎曼曲面。我们发现任意属的表面上的分区函数可以通过对适用于环面的规则的直接概括来构造。我们演示了如何使用这些更高的属对象来计算基础理论中的相关函数和 OPE 系数。在连续对称子群的自由玻色子理论的轨道的情况下，我们可以给出我们的程序的明确结果，用于循环群的对称和非对称轨道。