# Maximally supersymmetric amplitudes at infinite loop momentum

Bourjaily, Jacob L. (Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark) ; Herrmann, Enrico (SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94039, USA) ; Trnka, Jaroslav (Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA)

15 March 2019

Abstract: We investigate the asymptotically large loop-momentum behavior of multiloop amplitudes in maximally supersymmetric ($N=4$, 8) quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in $N=4$ 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 $N=8$ 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.

Published in: Physical Review D 99 (2019)
Published by: APS
DOI: 10.1103/PhysRevD.99.066006
arXiv: 1812.11185
License: CC-BY-4.0

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