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A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons20678

Beisert,  Niklas
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Dippel,  Viginia
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20717

Staudacher,  Matthias
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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205038.pdf
(Preprint), 545KB

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Citation

Beisert, N., Dippel, V., & Staudacher, M. (2004). A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills. Journal of High Energy Physics, 2004(7): 075. Retrieved from http://www.iop.org/EJ/abstract/1126-6708/2004/07/075.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-51A9-C
Abstract
We probe the long-range spin chain approach to planar = 4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the (2) subsector of the state space up to three loops, but ceases to exhibit the conjectured thermodynamic scaling properties at higher orders. We indicate how this may be bypassed while nevertheless preserving integrability, and suggest the corresponding all-loop asymptotic Bethe ansatz. We also propose the local part of the all-loop gauge transfer matrix, leading to conjectures for the asymptotically exact formulae for all local commuting charges. The ansatz is finally shown to be related to a standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical string theory uncovers a detailed, non-perturbative agreement between the corresponding expressions for the infinite tower of local charge densities. However, the respective Bethe equations differ slightly, and we end by refining and elaborating a previously proposed possible explanation for this disagreement.