The Resurgence of the Cusp Anomalous Dimension

Abstract: This work addresses the resurgent properties of the cusp anomalous dimension's strong coupling expansion, obtained from the integral Beisert-Eden-Staudacher (BES) equation. This expansion is factorially divergent, and its first nonperturbative corrections are related to the mass gap of the $O(6)$ $\sigma$-model. The factorial divergence can also be analysed from a resurgence perspective. Building on the work of Basso and Korchemsky, a transseries ansatz for the cusp anomalous dimension is proposed and the corresponding expected large-order behaviour studied. One finds non-perturbative phenomena in both the positive and negative real coupling directions, which need to be included to address the analyticity conditions coming from the BES equation. After checking the resurgence structure of the proposed transseries, it is shown that it naturally leads to an unambiguous resummation procedure, furthermore allowing for a strong/weak coupling interpolation.