Exact results for perturbative Chern-Simons theory with complex gauge group.
Exact results for perturbative Chern-Simons theory with complex gauge group.
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具有复杂规范群的微扰陈-西蒙斯理论的精确结果。
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
D. Zagier
中科院分区：
文献类型：
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作者：
Tudor Dimofte;S. Gukov;J. Lenells;D. Zagier
我们发展了几种方法，使我们能够计算具有复规范群G_C的微扰Chern-Simons理论中的全圈配分函数，
以多种方式。在非交换不可约平坦联络的背景下，微扰G_C不变量是一种有趣的拓扑不变量，它与紧规范群G理论中的有限型（Vassiliev）不变量有很大的不同.我们探讨这些不变量的各个方面，并提出了一个例子，我们明确地计算高循环顺序。我们还介绍了“算术TQFT”的概念和猜想（支持数值证据），SL（2，C）陈-西蒙斯理论是这样一个理论的一个例子。
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes
in multiple ways. In the background of a non-abelian irreducible flat connection, perturbative G_C invariants turn out to be interesting topological invariants, which are very different from finite type (Vassiliev) invariants obtained in a theory with compact gauge group G. We explore various aspects of these invariants and present an example where we compute them explicitly to high loop order. We also introduce a notion of “arithmetic TQFT” and conjecture (with supporting numerical evidence) that SL(2,C) Chern-Simons theory is an example of such a theory.