U(N) torus link invariants in the large N limit from the matrix model approach

In this paper we study U(N) colored HOMFLY-PT polynomials of torus links in the double scaling limit (polynomial variable q→1, N→∞ keeping qN fixed). We show that, in this limit, the colored HOMFLY-PT polynomial of any (Lα,Lβ) torus link can be expressed in terms of the colored HOMFLY-PT polynomial of (L,L) torus link. Using the connection between matrix models and the Chern-Simons field theoretic invariants, we show that the colored torus link invariants are uniquely expressed in terms of connected correlation functions of operators in U(N) matrix model. We determine the leading and subleading contribution to some of the correlators at large N from the matrix model approach and find that they match exactly with those obtained from the corresponding colored HOMFLY-PT polynomials. Published by the American Physical Society 2024