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We discuss the near BPS expansion of the generalized cusp anomalous dimensionwith L units of R-charge. Integrability provides an exact solution, obtained bysolving a general TBA equation in the appropriate limit: we propose here analternative method based on supersymmetric localization. The basic idea is torelate the computation to the vacuum expectation value of certain 1/8 BPSWilson loops with local operator insertions along the contour. Theseobservables localize on a two-dimensional gauge theory on S^2, opening thepossibility of exact calculations. As a test of our proposal, we reproduce theleading Luscher correction at weak coupling to the generalized cusp anomalousdimension. This result is also checked against a genuine Feynman diagramapproach in N=4 Super Yang-Mills theory.

Bremsstrahlung function, leading Luscher correction at weak coupling and localization