Universal character, phase model and topological strings on pmb {mathbb {C}^3}

Na Wang,Chuanzhong Li

doi:10.1140/epjc/s10052-019-7483-z

Na Wang, Chuanzhong Li

Open Access

https://doi.org/10.1140/epjc/s10052-019-7483-z

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Abstract

In this paper, we consider two different subjects: the algebra of universal characters S_{[lambda ,mu ]}(mathbf{x},mathbf{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.

Highlights

Symmetric functions were used to determine irreducible characters of highest weight representations of the classical groups [1]
The universal character, as a generalization of Schur function, describes the character of an irreducible rational representation of G L(n) [2], which upgrades that Schur function is the character of an irreducible polynomial representation of G L(n)
Tsuda defined the UC hierarchy which is a generalization of KP hierarchy and obtained that the tau functions of UC hierarchy can be realized in terms of the universal characters

Summary

Introduction

Symmetric functions were used to determine irreducible characters of highest weight representations of the classical groups [1]. The actions of creation operators B1(u) and B2(u), which are entries in the monodromy matrix T (u) of the phase model, on universal characters are determined by the truncated expansions of 1−(z) and 2−(z) respectively, and the annihilation operators C1(u) and C2(u) (multiplied by a coefficient) are adjoint to the operators B1(u) and B2(u), and determined by the truncated expansions of 1+(z) and Another purpose of this paper is to discuss the relations between the vertex operators i−(z),. 4, we define the representation of the two-site generalized phase model on the algebra of universal characters, and we find that the actions of the entries in monodromy matrix on universal characters are obtained from the truncated expansions of the vertex operators discussed in Sect.

Universal characters and vertex operators

Phase model

Two-site generalized phase model and universal characters

Vertex operators and topological strings on C3