N Beisert and T Klose J. Stat. Mech. (2006) P07006 doi:10.1088/1742-5468/2006/07/P07006
Long-range 
integrable spin chains and plane-wave matrix theory
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Topical articles on The 75th Anniversary of the Bethe Ansatz
N Beisert1 and T Klose2,3
Show affiliationsPart of Topical articles on The 75th Anniversary of the Bethe Ansatz
Quantum spin chains arise naturally from perturbative large-N field theories and matrix models. The Hamiltonian of such a model is a long-range deformation of nearest-neighbour type interactions. Here, we study the most general long-range integrable spin chain with spins transforming in the fundamental representation of . We derive the Hamiltonian and the corresponding asymptotic Bethe ansatz at the leading four perturbative orders with several free parameters. Furthermore, we propose Bethe equations for all orders and identify the moduli of the integrable system. We finally apply our results to plane-wave matrix theory and show that the Hamiltonian in a closed sector is not of this form and therefore not integrable beyond the first perturbative order. This also implies that the complete model is not integrable.
- A commentary on this article has been published by Sakura Schäfer-Nameki, 2006 J. Stat. Mech. N12001.
- Keywords
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E-print Number: hep-th/0510124
Cited: by |
Refers: to
- PACS
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11.15.Pg Expansions for large numbers of components (e.g., 1/Nc expansions)
- MSC
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81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)
81R12 Relations with integrable systems (See also 17Bxx, 37J35)
81T40 Two-dimensional field theories, conformal field theories, etc.
- Subjects
- Dates
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Issue 07 (July 2006)
Received 3 June 2006, accepted for publication 26 June 2006
Published 17 July 2006
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Long-range integrable spin chains and plane-wave matrix theory
N Beisert and T Klose J. Stat. Mech. (2006) P07006
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