  The cusp anomalous dimension is a ubiquitous quantity in four-dimensional
gauge theories, ranging from QCD to maximally supersymmetric N=4 Yang-Mills
theory, and it is one of the best investigated observables in the AdS/CFT
correspondence. In planar N=4 SYM theory, its perturbative expansion at weak
coupling has a finite radius of convergence while at strong coupling it admits
an expansion in inverse powers of the 't Hooft coupling which is given by a
non-Borel summable asymptotic series. We study the cusp anomalous dimension in
the transition regime from strong to weak coupling and argue that the
transition is driven by nonperturbative, exponentially suppressed corrections.
To compute these corrections, we revisit the calculation of the cusp anomalous
dimension in planar N=4 SYM theory and extend the previous analysis by taking
into account nonperturbative effects. We demonstrate that the scale
parameterizing nonperturbative corrections coincides with the mass gap of the
two-dimensional bosonic O(6) sigma model embedded into the AdS_5xS^5 string
theory. This result is in agreement with the prediction coming from the string
theory consideration.
