Chern-Simons theory is a 3D topological QFT: Z=∫DA exp(ik/4π ∫Tr(A∧dA+⅔A∧A∧A)). Wilson loops W_R(K)=Tr P exp(∮_K A) are the observables — their expectation values give knot invariants including the Jones polynomial at q=e^(2πi/(k+2)).
Knot Selector
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Wilson loop:
W_R(K)=Tr P exp(∮A)
Jones polynomial:
⟨W⟩_CS = V_K(q)
q=e^(2πi/(k+2))
Framing anomaly:
Writhe shift by n
multiplies by q^(nθ)