报告题目: |
A discretized Chern-Simons gauge theory on arbitrary graphs |
报告人: |
Kai Sun |
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University of Michigan
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报告时间: |
2015-06-17 14:30 |
报告地点: |
Conference Hall 322, Science Building, Tsinghua University |
主办单位: |
高等研究院 |
简介: |
In this talk, I will show how to discretize the 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. |
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