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Journal of Physics A Mathematical and Theoretical

Deformation of Wess–Zumino–Witten fusion rules from open q -boson models with diagonal boundary conditions*

J. F. van Diejen

Published Jun 17, 2020• 4 citations
Publisher

Abstract

Abstract It is known from work of Korff that the q -boson model with periodic boundary conditions gives rise to a q -deformation of the Wess–Zumino–Witten fusion algebra of type  . We employ recent results on the diagonalization of a finite aperiodic q -boson model with diagonal open end boundary conditions, so as to construct an analogous deformation of the Wess–Zumino–Witten fusion algebra of type B C ̂ .

DOI
10.1088/1751-8121/ab977f

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Abstract It is known from work of Korff that the q -boson model with periodic boundary conditions gives rise to a q -deformation of the Wess–Zumino–Witten fusion algebra of type  . We employ recent results on the diagonalization of a finite aperiodic q -boson model with diagonal open end boundary conditions, so as to construct an analogous deformation of the Wess–Zumino–Witten fusion algebra of type B C ̂ .
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Off-diagonal Bethe Ansatz for the D3(1) {D}_3^{(1)} D3(1)​ model
Abstract The exact solutions of the D3(1) {D}_3^{(1)} D3(1)​ D 3 1 model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the T - Q relations for the periodic case and by the inhomogeneous T- Q one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the Dn(1) {D}_n^{(1)} Dn(1)​ D n 1 model directly.
Open descendants extend Conformal Field Theory to unoriented surfaces with boundaries. The construction rests on two types of generalizations of the fusion algebra. The first is needed even in the relatively simple case of diagonal models. It leads to a new tensor that satisfies the fusion algebra, but whose entries are signed integers. The second is needed when dealing with non-diagonal models, where Cardy's ansatz does not apply. It leads to a new tensor with positive integer entries, that satisfies a set of polynomial equations and encodes the classification of the allowed boundary operators.
Abstract The B 1 vertex model is studied by the off-diagonal Bethe ansatz method. New closed operator product identities of the fused transfer matrices are obtained by using the fusion technique. Based on them and the asymptotic behaviors as well as the values of the fused transfer matrices at certain points, the exact solutions of the B 1 model with periodic and with integrable off-diagonal open boundary conditions are obtained. We find that the degree of the polynomial of the inhomogeneous T − Q relation is lower. The B 1 model is equivalent to the integrable spin-1 Heisenberg chain, thus the method and the results in this paper can be generalized to the high spin Heisenberg model and the integrable models associated with B n Lie algebra.