Hopf link invariants and integrable hierarchies
Chuanzhong Li, А. Миронов, A. Yu. Orlov
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 τ -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 τ -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.
Topics & Concepts
PhysicsLink (geometry)Integrable systemHopf algebraMathematical physicsParticle physicsPure mathematicsTheoretical physicsAlgebra over a fieldQuantum mechanicsQuantumCombinatoricsMathematicsAlgebraic structures and combinatorial modelsGeometric and Algebraic TopologyNonlinear Waves and Solitons