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.
