Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-05-03
JHEP 0407:075,2004
Physics
High Energy Physics
High Energy Physics - Theory
48 pages, 1 figure. v2, further results added: discussion of the relationship to an inhomogeneous spin chain, normalization in
Scientific paper
10.1088/1126-6708/2004/07/075
We probe the long-range spin chain approach to planar N=4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the SU(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.
Beisert Niklas
Dippel V.
Staudacher Matthias
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