Analytic all-plus-helicity gluon amplitudes in QCD

We detail the calculation of two-loop all-plus-helicity amplitudes for pure Yang-Mills theory. The four-dimensional unitarity methods and augmented recursion techniques we have developed, together with a knowledge of the singular structure of the amplitudes, allow us to compute these in compact analytic forms. Specifically we present the computation and analytic results for the six- and seven-gluon leading color two-loop amplitudes, these being the first QCD two-loop amplitudes beyond five points.