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Using an iterative solution of rapidity evolution equations, we computepartonic $2\to 2$ gauge theory amplitudes at four loops in full colour up tothe Next-to-Next-to-Leading Logarithms (NNLL) in the Regge limit. Bycontrasting the resulting amplitude with the exponentiation properties of softsingularities we determine the four-loop correction to the soft anomalousdimension at this logarithmic accuracy, which universally holds in any gaugetheory. We find that the latter features quartic Casimir contributions beyondthose appearing in the cusp anomalous dimension. Finally, in the case of ${\calN}=4$ super Yang-Mills, we also determine the finite hard function at fourloops through NNLL in full colour.

Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour