Spin models and superconformal Yang-Mills theory

We apply novel techniques in planar superconformal Yang-Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local Abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability.