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

Abstract

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.

22 pages, v2: reference added

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• A Yangian Double for the AdS/CFT Classical r-matrix
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• Irrelevant Deformations with Boundaries and Defects
• Wrapping corrections for long range spin chains
• Integrability and the AdS/CFT correspondence
• Entanglement propagation and dynamics in non-additive quantum systems
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• Four-loop anomalous dimensions in Leigh-Strassler deformations
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