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

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

2007-11-29

arxiv.org/abs/0711.4813v3

J.Stat.Mech.0803:P03001,2008

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1742-5468/2008/03/P03001

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.

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