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arxiv: 1001.2003 · v2 · pith:NNVEPUVXnew · submitted 2010-01-12 · ✦ hep-th

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

classification ✦ hep-th
keywords invariantsr-matrixtheorychern-simonscontributegaugeknotplane
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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^{\rho}.

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