Off-Shell Bethe Ansatz Equation for Gaudin Magnets and Solutions of Knizhnik-Zamolodchikov Equations

Abstract

We generalize the previously established connection between the off-shell Bethe ansatz equation for inhomogeneous SU(2) lattice vertex models in the quasiclassical limit and the solutions of the SU(2) Knizhnik-Zamolodchikov equations to the case of simple Lie algebras of higher rank.

Chern–Simons theory and BCS superconductivity

“…The similarity between the works [12] and [16,17] suggested that the Richardson's solution of the reduced BCS model should also be derivable using the off-shell Bethe ansatz method. This was done by Amico, Falci and Fazio [18] and later on clarified in references [19,20,21], where the BCS coupling constant parametrizes a boundary operator that appears in the transfer matrix of the inhomogenous vertex model, whose semi-classical limit gives rise to the CRS conserved quantities.…”

Integrability and Conformal Symmetry in the BCS Model

“…The CFT interpretation of the BCS model, explained in the previous section, turns out to be closely related to the works of Babujian [22], and Babujian, Flume [23] who in 1993 rederived Gaudin's exact solution using the so called off-shell algebraic Bethe ansatz (OSBA). These authors also pointed out that Gaudin's eigenstates can be used to build the conformal blocks of the WZW models, along the same lines as was shown in the previous section.…”

“…The similarity between the works [10] and [22,23] suggested that the Richardson's solution of the reduced BCS model should also be derivable using the OSBA method. This was done by Amico, Falci and Fazio [24], and later on clarified in references [25,26,27], where the BCS coupling constant parametrizes a boundary operator that appears in the transfer matrix of the inhomogenous vertex model, whose semi-classical limit gives rise to the CRS conserved quantities.…”

Multiple orthogonal polynomials and a counterexample to the Gaudin Bethe Ansatz Conjecture

“…The Hamiltonians commute. The problem is to diagonalize simultaneously the Hamiltonians; see [B,BF,FFR,G,MV1,RV,ScV,V2].…”