Abstract
We revisit the strong coupling limit of the cusp anomalous dimension in planar \( \mathcal{N}=4 \) super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling pertur- bative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors, and the final result is real and unambiguous.
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Dorigoni, D., Hatsuda, Y. Resurgence of the cusp anomalous dimension. J. High Energ. Phys. 2015, 138 (2015). https://doi.org/10.1007/JHEP09(2015)138
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DOI: https://doi.org/10.1007/JHEP09(2015)138