Geodesic
Eden--Staudacher and Beisert--Eden--Staudacher equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 117-129

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We investigate the Eden–Staudacher and Beisert–Eden–Staudacher equations for the anomalous dimension of twist-$2$ operators at a large spin $s$ in the $\mathcal{N}{=}4$ supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions $\zeta(k)$ having the maximum transcendentality property. We also show that at a large coupling, the "singular" solution of the Beisert–Eden–Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT correspondence.
Mots-clés : anomalous dimension
Keywords: $\mathcal{N}{=}4$ supersymmetric gauge theory. 
@article{TMF_2008_155_1_a9,
     author = {A. V. Kotikov and L. N. Lipatov},
     title = {Eden--Staudacher and {Beisert--Eden--Staudacher} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {117--129},
     publisher = {mathdoc},
     volume = {155},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a9/}
}
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A. V. Kotikov; L. N. Lipatov. Eden--Staudacher and Beisert--Eden--Staudacher equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 1, pp. 117-129. http://geodesic.mathdoc.fr/item/TMF_2008_155_1_a9/