Topological Recursion and Mirror Symmetry in Chern-Simons Wilson Loops — E8 Intelligence Research

FINDING: Wilson loop expectation values in Chern-Simons theory are governed by topological recursion and mirror symmetry, linking gauge theory invariants to algebraic curve moduli. MATH: - Chern-Simons action: \( SCS = k/4π ∫_M Tr(A dA + 2/3 A A A) \) - Wilson loop expectation: \( W_R(K) = ∫ [DA] \, e^{iSCS} \, Tr_R \, Pexp(∮_K A) \) - Topological recursion: \( ωg,n \) on spectral curve \( Σ \) (algebraic curve with modular properties) - Mirror symmetry: Gopakumar-Ooguri-Vafa duality maps CS invariants to Gromov-Witten invariants of resolved conifold, with \( t = 2π i/k+N \) ('t Hooft coupling). - Seifert loop invariants: \( W_R(Seifert) \) related to quantum \( sl_N \) invariants at \( q = e2π i/(k+N) \). CONNECTION: - Modular forms appear via spectral curve \( Σ \) (e.g., \( y^2 = x^3 + ax + b \) with modular para Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com