Integrable Spin Models and Superconformal Yang-Mills Theory

Planar superconformal Yang-Mills theory in four dimensions has yielded to a partial description in terms of integrable spin model structures. It is compelling to ask how much more of the gauge theory can be cast in integrable forms that could eventually reveal the exact spectrum and correlation functions. We apply novel techniques that focus on 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.