Chern-Simons Theory with SU(N) and AN-1 Lattice: Knot Invariants and TQFT — E8 Intelligence Research

FINDING: Chern-Simons theory with SU(N) gauge group and AN-1 root lattice defines a topological quantum field theory (TQFT) whose partition function yields knot invariants and links to modular tensor categories. | MATH: Chern-Simons action: \( SCS = k/4π ∫_M Tr(A dA + 2/3 A A A) \), where \( A \) is a connection on a principal SU(N) bundle over a 3-manifold \( M \), \( k ∈ Z \) is the level. The root lattice \( AN-1 \) corresponds to the Lie algebra \( su(N) \), with simple roots \( α_i \) (\( i=1,,N-1 \)) and Cartan matrix \( Cᵢⱼ = 2 α_i, α_j / α_i, α_i \). The theory is topological (metric-independent) and its Hilbert space on a torus is the space of conformal blocks of the Wess-Zumino-Witten model, with dimension given by the Verlinde formula: \( HT^2 = ∑λ ( {S0λ}{S₀₀} )² \), wher Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com