Proof of the Labastida-Mariño-Ooguri-Vafa conjecture

Abstract

Based on large $N$ Chern-Simons/topological string duality, in a series of papers, Labastida, Mariño, Ooguri, and Vafa conjectured certain remarkable new algebraic structure of link invariants and the existence of infinite series of new integer invariants. In this paper, we provide a proof of this conjecture. Moreover, we also show these new integer invariants vanish at large genera.