G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra

TL;DR

This paper explores the deep connection between G/G gauged WZW models, q-boson models, and Frobenius algebras, revealing how topological gauge theories encode quantum integrable systems and their algebraic structures.

Contribution

It introduces a one-parameter deformation linking gauged WZW models with q-boson models and analyzes their relation through the framework of commutative Frobenius algebras.

Findings

G/G gauged WZW model corresponds to the phase model

Deformation relates gauged WZW to q-boson model

Frobenius algebra provides an algebraic perspective on the correspondence

Abstract

We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from a viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.