We present unitarity as a method for determining the infinities present in graviton scattering amplitudes. The infinities are a combination of IR and UV. By understanding the soft singularities we may extract the UV infinities and relate these to counter-terms in the effective action. As an demonstration of this method we rederive the UV infinities present at one-loop when gravity is coupled to matter.
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Dunbar et al. (1997) studied this question.