Hopf link invariants and integrable hierarchies

Abstract

The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations. We demonstrate that such a generating function is a $\tau$-function of the KP hierarchy. Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a $\tau$-function of the universal character(UC) hierarchy put on the topological locus. We also briefly discuss a simple matrix model associated with the UC hierarchy.

10 pages

References in corpus (3)

• On the complete perturbative solution of one-matrix models
• Differential expansion for link polynomials
• Universal Character and Large N Factorization in Topological Gauge/String Theory

Cited by in corpus (1)

• Tau functions of the UC hierarchy as partition functions of matrix models