Mirror Symmetry Duality Links Chern-Simons Theory to Topological Strings — E8 Intelligence Research

FINDING: Mirror symmetry establishes a duality between Chern-Simons theory on a 3-manifold and topological string theory on a Calabi-Yau 3-fold, linking knot invariants to homological invariants via the topological recursion. | MATH: Chern-Simons path integral \( Z_{CS}(M) = \int \mathcal{D}A \, e^{i k S_{CS}[A]} \) with \( S_{CS}[A] = \frac{1}{4\pi} \int_M \text{Tr}(A \wedge dA + \frac{2}{3} A \wedge A \wedge A) \); Gopakumar-Ooguri-Vafa duality maps \( Z_{CS}(M) \) to Gromov-Witten invariants of a mirror Calabi-Yau; topological recursion yields \( \omega_{g,n} \) from spectral curve data; homological invariants (e.g., Khovanov homology) categorify quantum knot invariants. | CONNECTION: Mirror symmetry involves root systems of Lie algebras (e.g., \( A_n, D_n, E_8 \)) and their Weyl groups, which are crystallographic; the spectral curve often exhibits ratios like \( e^{2\pi i \tau} \) with modular parameter \( \tau \), linking to base-60 (sexagesimal) via Babylonian approximations of \ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com