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

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.

41 pages, 7 figures, Published version

References in corpus (4)

• Higgs Bundles, Gauge Theories and Quantum Groups
• Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Volume of Moduli Space of Vortex Equations and Localization

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