Nonperturbative scales in AdS/CFT

TL;DR

This paper investigates the transition of the cusp anomalous dimension in N=4 SYM from strong to weak coupling, revealing that nonperturbative effects, linked to the O(6) sigma model's mass gap, drive this transition.

Contribution

The study extends previous analyses by incorporating nonperturbative effects into the calculation of the cusp anomalous dimension in AdS/CFT.

Findings

Nonperturbative corrections are exponentially suppressed.

The nonperturbative scale matches the O(6) sigma model's mass gap.

Results align with string theory predictions.

Abstract

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.