Universal Character, Phase Model and Topological Strings on $\mathbb C^3$

TL;DR

This paper explores the connections between universal characters, a phase model of bosons, and topological string theory on ^3, revealing how algebraic structures can model physical systems and compute string partition functions.

Contribution

It demonstrates that the algebra of universal characters can realize the phase model and generate topological string partition functions on ^3.

Findings

Universal characters can represent the phase model's monodromy matrix entries.

Vertex operators generate universal characters and compute topological string partition functions.

The phase model is connected to topological string theory via algebraic structures.

Abstract

In this paper, we consider two different subjects: the algebra of universal characters $S_{[\lambda,\mu]}({\bf x},{\bf y})$ (a generalization of Schur functions) and the phase model of strongly correlated bosons. We find that the two-site generalized phase model can be realized in the algebra of universal characters, and the entries in the monodromy matrix of the phase model can be represented by the vertex operators $\Gamma_i^\pm(z) (i=1,2)$ which generate universal characters. Meanwhile, we find that these vertex operators can also be used to obtain the A-model topological string partition function on $\mathbb C^3$.