Planar N=4 gauge theory and the Inozemtsev long range spin chain
Abstract
We investigate whether the (planar, two complex scalar) dilatation operator of Script N = 4 gauge theory can be, perturbatively and, perhaps, non-perturbatively, described by an integrable long range spin chain with elliptic exchange interaction. Such a chain was introduced some time ago by Inozemtsev. In the limit of sufficiently ``long'' operators a Bethe ansatz exists, which we apply at the perturbative two- and three-loop level. Spectacular agreement is found with spinning string predictions of Frolov and Tseytlin for the two-loop energies of certain large charge operators. However, we then go on to show that the agreement between perturbative gauge theory and semi-classical string theory begins to break down, in a subtle fashion, at the three-loop level. This corroborates a recently found disagreement between three-loop gauge theory and near plane-wave string theory results, and quantitatively explains a previously obtained puzzling deviation between the string proposal and a numerical extrapolation of finite size three-loop anomalous dimensions. At four loops and beyond, we find that the Inozemtsev chain exhibits a generic breakdown of perturbative BMN scaling. Finally we suggest, assuming the AdS/CFT correspondence to be dynamically correct, that the observed three-loop disagreement between string and gauge theory might find an explanation as an order of limits (weak versus strong 't Hooft coupling) problem.
- Publication:
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Journal of High Energy Physics
- Pub Date:
- June 2004
- DOI:
- 10.1088/1126-6708/2004/06/001
- arXiv:
- arXiv:hep-th/0401057
- Bibcode:
- 2004JHEP...06..001S
- Keywords:
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- AdS-CFT and dS-CFT Correspondence Bethe Ansatz;
- High Energy Physics - Theory
- E-Print:
- 31 pages, no figure