We investigate the asymptotically large loop-momentum behavior of multiloop amplitudes in maximally supersymmetric ($\mathcal{N}=4$, 8) quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in $\mathcal{N}=4$ supersymmetric Yang-Mills theory to demonstrate the absence of poles at infinity of all $n$-point MHV amplitudes through three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads us to discover that this theory does support nonvanishing residues at infinity starting at two loops, and the degree of these poles grow arbitrarily with multiplicity. This causes a tension between simultaneously manifesting ultraviolet finiteness—which would be automatic at two loops for representation obtained by color-kinematic duality—and gauge invariance—which would follow from unitarity-based methods.

• Received 7 January 2019

DOI:https://doi.org/10.1103/PhysRevD.99.066006

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Published by the American Physical Society