We revisit the strong coupling limit of the cusp anomalous dimension in planar N=4N=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.
Dorigoni, D., & Hatsuda, Y. (2015). Resurgence of the cusp anomalous dimension. Journal of High Energy Physics, 2015(09), Article 138. https://doi.org/10.1007/jhep09%282015%29138