Knots, links and branes at large N

TL;DR

This paper explores the duality between large N Chern-Simons theory and topological string theory, focusing on links, and introduces refined invariants based on brane representation degeneracies, supported by explicit calculations.

Contribution

It extends the large N duality checks to links, revealing a new structure involving brane degeneracies and refining link and knot invariants.

Findings

Identification of representation/spin degeneracy in branes

Refinement of integer invariants for links and knots

Explicit computations confirming the duality and invariants

Abstract

We consider Wilson loop observables for Chern-Simons theory at large N and its topological string dual and extend the previous checks for this duality to the case of links. We find an interesting structure involving representation/spin degeneracy of branes ending on branes which features in the large N dual description of Chern-Simons theory. This leads to a refinement of the integer invariants for links and knots. We illustrate our results with explicit computations on the Chern-Simons side.