D-branes and the planar limit of Chern-Simons theory I: Link invariants

We revisit the Holographic duality between $SU(N{)}_{\kappa }$ Chern-Simons theory and the A-model Topological String Theory. We develop a strategy to systematically compute the large $N$ saddles for correlation functions of Wilson lines in antisymmetric powers ${\mathrm{\Lambda }}^{\bullet }{\mathbb{C}}^N$ of the fundamental representation. The mathematical structures which appear in the calculation match in detail the data of dual A-model D-branes.