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Eden-Staudacher and Beisert-Eden-Staudacher equations in the \(\mathcal{N} = 4\) supersymmetric gauge theory

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Abstract

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 ζ(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.

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Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

    A. V. Kotikov

  2. Konstantinov Petersburg Nuclear Physics Institute, RAS, Gatchina, Leningrad Oblast, Russia

    L. N. Lipatov

  3. Institut für Theoretische Physik, Universität Hamburg, Hamburg, Germany

    L. N. Lipatov

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  1. A. V. Kotikov
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  2. L. N. Lipatov
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Correspondence to A. V. Kotikov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 117–129, April, 2008.

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Kotikov, A.V., Lipatov, L.N. Eden-Staudacher and Beisert-Eden-Staudacher equations in the \(\mathcal{N} = 4\) supersymmetric gauge theory. Theor Math Phys 155, 606–617 (2008). https://doi.org/10.1007/s11232-008-0050-7

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