Higher Charges in Dynamical Spin Chains for SYM Theory

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.

14 pages; V2: Appendix added with diagrammatic expression for H_{3,2}

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Cited by in corpus (7)

• N=4 SYM to Two Loops: Compact Expressions for the Non-Compact Symmetry Algebra of the su(1,1|2) Sector
• Open Spin Chains in Super Yang-Mills at Higher Loops: Some Potential Problems with Integrability
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• The su(2|3) Undynamic Spin Chain
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling