The analytic Bethe ansatz for a chain with centrally extended su(2|2) symmetry

We investigate the integrable structure of spin chain models with centrally extended su( 2 vertical bar 2) and psu( 2, 2 vertical bar 4) symmetry. These chains have their origin in the planar anti-de Sitter/conformal field theory correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su( 2 vertical bar 2). These results are applied in the construction and investigation of an interesting S-matrix with su( 2 vertical bar 2) symmetry. In particular, they enable a remarkably simple proof of the Yang-Baxter relation. We also show the equivalence of the S-matrix to Shastry's R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix eigenvalues for models with psu( 2, 2 vertical bar 4) symmetry is sketched.