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arXiv 1001.2003hep-th
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通过普适量子R-矩阵的时间规范和纽结不变量的Chern-Simons理论

Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix

Alexei Morozov, Andrey Smirnov

摘要:

在时间规范A_{0} =0中,3d Chern-Simons理论获得了二次作用量和超局域传播子。这直接意味着威尔逊线的分解子(结不变量)的2D R矩阵表示,其中仅xy平面上的轮廓投影的交叉点有贡献。虽然理论是二次的,P-指数仍然是非平凡的算子,R-因子更容易猜测,然后推导。我们证明了如果引入附加的标志结构(xy平面和其中的一条y线),R是泛量子R-矩阵,并且转向点贡献了“增强”因子q^ρ,则拓扑不变量出现。

英文摘要:

In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing points of the contours projection on the xy plane contribute. Though the theory is quadratic, P-exponents remain non-trivial operators and R-factors are easier to guess then derive. We show that the topological invariants arise if additional flag structure (xy plane and an y line in it) is introduced, R is the universal quantum R-matrix and turning points contribute the "enhancement" factors q^ρ.

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