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A previously proposed all-loop-orders relation between the Regge limits offour-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8supergravity is established at the three-loop level. We show that the Reggelimit of known expressions for the amplitudes obtained using generalizedunitarity simplifies in both cases to a (modified) sum over three-loop ladderand crossed-ladder scalar diagrams. This in turn is consistent with the resultobtained using the eikonal representation of the four-point gravity amplitude.A possible exact three-loop relation between four-point amplitudes is alsoconsidered.

Proof of a three-loop relation between the Regge limits of four-point amplitudes in N=4 SYM and N=8 supergravity