Understanding infrared singularities is essential in any multi-loop cross section calculation. It is also the key to resumming the dominant radiative corrections to all orders. I will review recent progress in understanding the infrared singularity structure in massless gauge theory amplitudes in dimensional regularization. I will describe the factorization of a general multi-leg amplitude into gauge invariant jet and soft functions using Wilson lines, and illustrate the relation between the infrared singularities of the amplitude and the renormalization properties of Wilson-line correlators. I will then focus on the soft function which correlates the colour flow with the kinematics, and show how the corresponding anomalous dimension is constrained to any loop order using a rescaling symmetry with respect to the Wilson line velocities and the cusp anomaly. I will then show that a remarkably simple sum-over-dipoles formula solves the constraints if the cusp anomalous dimension admits Casimir scaling, and discuss possible contributions going beyond this minimal solution.

Edinburgh University