The analytic Bethe ansatz for a chain with centrally extended symmetry

Abstract

We investigate the integrable structure of spin chain models with centrally extended and symmetry. These chains have their origin in the planar anti-de Sitter/conformal fieldtheory correspondence, but they also contain the one-dimensional Hubbard model as aspecial case. We begin with an overview of the representation theory of centrally extended. These results are applied in the construction and investigation of an interestingS-matrix with symmetry. In particular, they enable a remarkably simple proofof the Yang–Baxter relation. We also show the equivalence of theS-matrix toShastry’s R-matrix and thus uncover a hidden supersymmetry in the integrable structure of theHubbard model. We then construct eigenvalues of the corresponding transfer matrix inorder to formulate an analytic Bethe ansatz. Finally, the form of transfer matrixeigenvalues for models with symmetry is sketched.