Yangian Symmetry in D=4 Superconformal Yang-Mills Theory

TL;DR

This work establishes a concrete Yangian symmetry framework for four-dimensional ${\mathcal N}=4$ super Yang–Mills theory in the planar, weak-coupling regime. It proposes a bilinear nonlocal charge $Q^A = f^A_{BC} \sum_{i<j} J_i^B J_j^C$ that, in the $g^2N\to 0$ limit, commutes with the one-loop dilatation operator and generates an infinite set of conserved charges, linking to an integrable spin-chain picture of anomalous dimensions. The paper then develops the matrix-form representation of the Yangian for $SU(N)$, provides a practical criterion for when a single-site representation can realize the Yangian with $Q^A=0$, and shows how to bootstrap multi-spin representations via the coproduct $\Delta$. Finally, it extends the construction to the superalgebra $PSU(2,2|4)$, demonstrating that the bilinear $Q^A$ construction yields a valid Yangian representation for ${\mathcal N}=4$ SYM in the planar limit, thereby supporting the presence of Yangian symmetry in the AdS/CFT context.

Abstract

We will discuss an integrable structure for weakly coupled superconformal Yang-Mills theories, describe certain equivalences for the Yangian algebra, and fill a technical gap in our previous study of this subject.