任意图上离散化的Chern-Simons规范理论
A discretized Chern-Simons gauge theory on arbitrary graphs
摘要：
在本文中，我们展示了如何离散的阿贝尔陈-西蒙斯规范理论上的一般平面格/图（有或没有平移对称）嵌入任意二维封闭定向流形。我们发现，只要一个一对一的顶点和面孔之间的对应关系可以在图上定义，使每个面是配对与相邻顶点（反之亦然），离散化的陈-西蒙斯理论可以构建一致。我们进一步验证了离散化后的Chern-Simons规范理论的所有基本性质都保持不变。此外，我们发现，这样的一一对应的存在不仅是离散化的陈-西蒙斯规范理论的充分条件，但离散化的理论是非奇异的，并保持一些关键性质的拓扑场论，这种对应也是一个必要的。然后将提供一个具体的例子，其中我们离散的陈-西蒙斯规范理论的四面体。
英文摘要：
In this paper, we show how to discretize the abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary 2D closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Chern-Simons gauge theory on a tetrahedron.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
