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

TL;DR

This paper explores the holographic duality between Chern-Simons theory and topological string theory, developing methods to compute large N correlation functions of Wilson lines and matching mathematical structures with dual D-branes.

Contribution

It introduces a systematic approach to compute large N saddle points for Wilson line correlators and connects these calculations with dual D-brane data in topological string theory.

Findings

Successful computation of large N saddle points for Wilson line correlators.

Detailed matching of mathematical structures with dual D-branes.

Enhanced understanding of the holographic duality in Chern-Simons and topological string theories.

Abstract

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 $\Lambda^\bullet \mathbb{C}^N$ of the fundamental representation. The mathematical structures which appear in the calculation match in detail the data of dual A-model D-branes.