基于紧李群的拓扑量子场论
Topological Quantum Field Theories from Compact Lie Groups
摘要：
将三维Chern-Simons理论的定义扩展到将值与1-流形和0-流形相关联的定义是一个长期存在的问题。给出了规范群为环面时的一个解。我们还从不同的角度发展了一个相关的四维可逆拓扑域论，它编码了陈-西蒙斯的异常。有限规范群也重新审视，我们描述了一个理论的“有限路径积分“作为一个一般建设的某一类有限拓扑域论。低维拓扑纯规范理论作为热身。
英文摘要：
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also develop from different points of view an associated 4-dimensional invertible topological field theory which encodes the anomaly of Chern-Simons. Finite gauge groups are also revisited, and we describe a theory of "finite path integrals" as a general construction for a certain class of finite topological field theories. Topological pure gauge theories in lower dimension are presented as a warm-up.
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