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.
Highlights
WZW model coincides with that of the Chern-Simons theory [5, 6]
We investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory
As compared with (3.75), we find that the partition function of the commutative Frobenius algebra coincides with that of the SU(N )/SU(N ) gauged WZW-matter model up to the overall factor: h
Summary
We apply the algebraic Bethe Ansatz to the q-boson model. In particular, we construct the eigenvalues and the eigenstates of the Hamiltonian and give Bethe Ansatz equations. In order to apply the algebraic Bethe Ansatz method to the q-boson model, we first define an L-matrix and an R-matrix which satisfy the Yang-Baxter equation: R(μ, ν)(L(μ) ⊗ L(ν)) = (L(ν) ⊗ L(μ))R(μ, ν). We follow Slavnov’s derivation [20] of the inner product based on the commutation relations of the Yang-Baxter algebra, (2.14)– (2.20) An advantage of this method is to be able to apply to a wide class of models. When {μ1, · · · , μM } in (2.32) satisfies the Bethe Ansatz equations (2.27), we obtain ψ({λ}M )|ψ({λ}M ) = 0| C(λa) B(λa)|0 a=1 a=1 This norm will become one of the most important quantities when we study the Gauge/Bethe correspondence between the q-boson model and the topological field theory. We expect that the partition function of the G/G gauged WZW-matter model counts the number of the building blocks of a certain underlying field theory but we do not know what its field theory is
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