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

Understand

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}.