  A conjecture made by Bern, Dixon, Dunbar, and Kosower asserts a simple
dimension-shifting relationship between the one-loop structure of N = 4 MHV
amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. We prove
this conjecture to all orders in dimensional regularisation using unitarity
cuts, and evaluate the form of these simplest one-loop amplitudes using a
generalised D-dimensional unitarity technique which captures the full amplitude
to all multiplicities.
