Bremsstrahlung function, leading Luscher correction at weak coupling and localization

TL;DR

This paper introduces a localization-based method to compute the generalized cusp anomalous dimension in N=4 Super Yang-Mills theory, successfully reproducing the leading Luscher correction at weak coupling and offering an alternative to integrability-based solutions.

Contribution

It proposes a novel localization approach to calculate the cusp anomalous dimension, providing an exact method that complements integrability techniques.

Findings

Reproduces the leading Luscher correction at weak coupling.

Validates the localization method against Feynman diagram calculations.

Establishes a connection between Wilson loops with operator insertions and the cusp anomalous dimension.

Abstract

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.