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