Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory

Details Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory

2005-10-17

arxiv.org/abs/hep-th/0510124v2

J.Stat.Mech.0607:P07006,2006

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, v2: reference added

Scientific paper

10.1088/1742-5468/2006/07/P07006

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-neighbor type interactions. Here, we study the most general long-range integrable spin chain with spins transforming in the fundamental representation of gl(n). 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.

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