Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains

Abstract

An interesting type of spin chain has appeared in the context of the planar AdS/CFT correspondence: It is based on an integrable nearest-neighbor spin chain, and it is perturbatively deformed by long-range interactions which apparently preserve the integrable structure. Similar models can be constructed by demanding the existence of merely one conserved local charge. Although the latter is not a sufficient integrability condition in general, the models often display convincing signs of full integrability. Here we consider a class of long-range spin chains with spins transforming in the fundamental representation of gl(N). For the most general such model with one conserved local charge we construct a conserved Yangian generator and show that it obeys the Serre relations. We thus provide a formal proof of integrability for this class of models.

27 pages, v2: minor changes, references added, figures updated, v3: minor corrections, references added, to appear in JSTAT

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Cited by in corpus (17)

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• Exacting N=4 Superconformal Symmetry
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Lectures on Yangian Symmetry
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• Yangians, S-matrices and AdS/CFT
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• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Wrapping corrections for long range spin chains
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix