The two-loop amplitude (58) has been used by Green, Kwon, and Vanhove  to provide an explicit demonstration of the non-trivial M-theory duality between supergravity and type II string theory. In this case, the finite parts of the supergravity amplitudes are important, particularly the way they depend on the radii of compactified dimensions.
A remarkable feature of the two-particle cutting equation (56) is that it can be iterated to all loop orders because the tree amplitude (times some scalar denominators) reappears on the right-hand side. Although this iteration is insufficient to determine the complete multi-loop four-point amplitudes, it does provide a wealth of information. In particular, for planar integrals it leads to the simple insertion rule depicted in Figure 13 for obtaining the higher loop contributions from lower loop ones . This class includes the contribution in Figure 4, because it can be assembled entirely from two-particle cuts. According to the insertion rule, the contribution corresponding to Figure 4 is given by loop integrals containing the propagators corresponding to all the internal lines multiplied by a numerator factor containing 8 powers of loop momentum. This is to be contrasted with the 24 powers of loop momentum in the numerator expected when there are no supersymmetric cancellations. This reduction in powers of loop momenta leads to improved divergence properties described in the next subsection.
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