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The four-loop cusp anomalous dimension in \( \mathcal{N} \) = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals

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Abstract

Correlation functions of Wilson lines are relevant for describing the infrared structure of scattering amplitudes. We develop a new method for evaluating a wide class of such Wilson line integrals, and apply it to the calculation of the velocity-dependent cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. We compute the four-loop non-planar correction in a recently introduced scaling limit. Moreover, we derive the full planar four-loop result by means of an ansatz which is based on the structure of known analytic results. We determine the coefficients in this ansatz by making use of a relationship to massive scattering amplitudes. As a corollary, our analytical result confirms the four-loop value of the light-like cusp anomalous dimension. Finally, we use the available perturbative data, as well as insight from AdS/CFT, in order to extrapolate the leading order values at strong coupling. The latter agree within two per cent with the corresponding string theory result, over a wide range of parameters.

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, NJ, 08540, U.S.A

    Johannes M. Henn

  2. Theoretische Physik 1, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Strasse 3, D-57068, Siegen, Germany

    Tobias Huber

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  1. Johannes M. Henn
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Henn, J.M., Huber, T. The four-loop cusp anomalous dimension in \( \mathcal{N} \) = 4 super Yang-Mills and analytic integration techniques for Wilson line integrals. J. High Energ. Phys. 2013, 147 (2013). https://doi.org/10.1007/JHEP09(2013)147

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