Higher Charges in Dynamical Spin Chains for SYM Theory

TL;DR

This paper constructs higher conserved charges in a dynamical spin chain model of N=4 Super Yang-Mills theory, testing integrability beyond static chains and proposing a diagrammatic approach for generalization.

Contribution

It introduces the first two non-trivial higher charges in a dynamical sector, advancing the understanding of integrability in N=4 SYM.

Findings

Constructed the first two higher conserved charges in the su(2|3) sector.

Demonstrated the algebraic and diagrammatic form of these charges.

Suggested the potential for generalization to full theory and higher loops.

Abstract

We construct, to the first two non-trivial orders, the next conserved charge in the su(2|3) sector of N=4 Super Yang-Mills theory. This represents a test of integrability in a sector where the interactions change the number of sites of the chain. The expression for the charge is completely determined by the algebra and can be written in a diagrammatic form in terms of the interactions already present in the Hamiltonian. It appears likely that this diagrammatic expression remains valid in the full theory and can be generalized to higher loops and higher charges thus helping in establishing complete integrability for these dynamical chains.