String Theory Journal Club

This talk investigates the reformulation of knot and link invariants as correlation functions in unitary matrix models, within the framework of Chern-Simons theory. In the double-scaling limit with fixed ’t Hooft coupling, Wilson loop operators simplify to trace insertions, enabling a systematic large N expansion of correlators. Leading and subleading contributions, structured through connected correlators, distinguish topological configurations and encode the interaction content of knot and link observables. Focusing on the Labastida–Marino–Ooguri–Vafa (LMOV) invariants, we analyze their generating function and compute the large N behavior of its coefficients, demonstrating that connected correlators contribute to key terms and reveal the asymptotic structure of the LMOV invariants.