Nonperturbative scales in AdS/CFT

Abstract

The cusp anomalous dimension is a ubiquitous quantityin four-dimensional gauge theories, ranging from QCD to maximally supersymmetric Yang–Mills theory, and it is one of the most thoroughly investigated observables in the AdS/CFT correspondence. In planar 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 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 AdS5 × S5 string theory. This result is in agreement with the prediction coming from the string theory consideration.