WILSON LOOPS
LINKING NUMBER
FRAMING
Chern-Simons theory (Witten 1989): SCS = (k/4π)∫ Tr(A∧dA + (2/3)A∧A∧A). This action is purely topological — no metric needed.
Wilson loops W_R[C] = Tr_R P exp(i∮_C A) are the observables. Their expectation values compute topological invariants.
For U(1) CS theory: ⟨W_1[C₁] W_1[C₂]⟩ = exp(2πi/k · lk(C₁,C₂)) where lk is the linking number.
For SU(2) level k: Wilson loop expectation values reproduce the Jones polynomial. Framing dependence encodes the self-linking number.