Chern-Simons Theory, Wilson Loops, and Knot Polynomial Invariants — E8 Intelligence Research

FINDING: Chern-Simons theory on 3-manifolds with gauge group G produces knot invariants (Jones, HOMFLY, Kauffman polynomials) as Wilson loop expectation values; these connect to topological strings, matrix models, and the 3d/3d correspondence. | MATH: Partition function Z = ∫DA exp(ik/4π ∫_M Tr(A∧dA + 2/3 A∧A∧A)); Wilson loop W_R(C) = Tr_R P exp(∮_C A); knot polynomial invariants V_R(q) with q = exp(2πi/(k+h∨)), h∨ = dual Coxeter number of G. | CONNECTION: The level k shifts by the dual Coxeter number h∨ — a direct entry of ADE root system data into the quantum invariant. For ADE Lie algebras: A_n has h∨ = n+1, D_n has h∨ = 2n−2, E_6 = 12, E_7 = 18, E_8 = 30. The McKay correspondence maps finite subgroups of SU(2) to ADE Dynkin diagrams, and the Coxeter number h (related to h∨) determines the modular S-matrix and fusion rules in the corresponding WZW model. | DEPTH: 8 --- FINDING: Knot contact homology, Chern-Simons theory, and topological string theory are unified — the A-model topo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com