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 amplitudesallow us to compute thesein compact analytic forms.Specifically we present the computation and analytic results for the six- and seven-gluon leading colour two-loop amplitudes these being the first QCD two-loop amplitudes beyond five-points