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Nonplanar contribution to the four-loop universal anomalous dimension of the twist-2 Wilson operators in the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory

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Abstract

The result of the direct component calculation of the nonplanar contribution to the four-loop anomalous dimension of the Konishi operator in the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory is reported. The result contains only the ζ(5) term proportional to the ζ(5) contribution in the planar case, which comes only from wrapping corrections. The previous calculations of the leading transcendent contribution to the anomalous dimension of the twist-2 operators for first three even moments are also expanded to the nonplanar case and the same results as in the planar case are obtained up to a general factor. These two results imply that the nonplanar contribution of the four-loop universal anomalous dimension of the twist-2 Wilson operators with an arbitrary Lorentz spin j is proportional to S 21 (j)ζ(5). This result provides a nonstandard square logarithmic asymptotic behavior ln2 j for large Lorentz spins j of the operators.

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  1. Theoretical Physics Department, Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, 188300, Russia

    V. N. Velizhanin

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Original Russian Text © V.N. Velizhanin, 2009, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 89, No. 12, pp. 697–700.

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Velizhanin, V.N. Nonplanar contribution to the four-loop universal anomalous dimension of the twist-2 Wilson operators in the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory. Jetp Lett. 89, 593–596 (2009). https://doi.org/10.1134/S0021364009120017

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