Chern-Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix

In temporal gauge A0=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 R3⊃R2⊃R1 (xy plane and a y line in it) is introduced, R is the universal quantum R-matrix and turning points contribute the “enhancement” factors qρ.