Universal Character and Large N Factorization in Topological Gauge/String Theory

TL;DR

This paper rigorously proves a large N factorization formula for the modular S-matrix in U(N) Chern-Simons theory, connecting topological gauge theory with universal characters and representation theory.

Contribution

It provides a rigorous proof of a previously proposed large N factorization formula using universal characters and specialized representations.

Findings

Established a formula for large N factorization of the modular S-matrix

Connected the factorization to universal characters for rational representations

Provided a rigorous proof based on character specialization

Abstract

We establish a formula of the large N factorization of the modular S-matrix for the coupled representations in U(N) Chern-Simons theory. The formula was proposed by Aganagic, Neitzke and Vafa, based on computations involving the conifold transition. We present a more rigorous proof that relies on the universal character for rational representations and an expression of the modular S-matrix in terms of the specialization of characters.