  We provide evidence in favor of the conjectured duality between color and
kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by
constructing a form of the one-loop four-point amplitude of this theory that
makes the duality manifest. Our construction is valid in any dimension. We also
describe a duality-satisfying representation for the two-loop four-point
amplitude with identical four-dimensional external helicities. We use these
results to obtain corresponding gravity integrands for a theory containing a
graviton, dilaton, and antisymmetric tensor, simply by replacing color factors
with specified diagram numerators. Using this, we give explicit forms of
ultraviolet divergences at one loop in four, six, and eight dimensions, and at
two loops in four dimensions.
