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

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

2010-01-12

arxiv.org/abs/1001.2003v2

Nucl.Phys.B 835:284-313, 2010

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 17 figures

Scientific paper

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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