Spin Models and Superconformal Yang-Mills Theory

TL;DR

This paper explores the role of Yangian algebra in planar superconformal Yang-Mills theory, computing key Casimirs and linking them to Hamiltonians, thereby advancing understanding of integrability in gauge theories.

Contribution

It introduces novel techniques to compute Yangian Casimirs and connects them to Hamiltonians, extending integrability analysis in superconformal Yang-Mills theory.

Findings

Computed the first two Yangian Casimirs.

Identified Casimirs with local Hamiltonians.

Extended R-matrix derivation to gauge theory.

Abstract

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.