Maximally supersymmetric amplitudes at infinite loop momentum

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

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.

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      "title": "Maximally supersymmetric amplitudes at infinite loop momentum"
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      "source": "APS", 
      "value": "We investigate the asymptotically large loop-momentum behavior of multiloop amplitudes in maximally supersymmetric (<math><mrow><mi>N</mi><mo>=</mo><mn>4</mn></mrow></math>, 8) quantum field theories in four dimensions. We check residue-theorem identities among color-dressed leading singularities in <math><mi>N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Yang-Mills theory to demonstrate the absence of poles at infinity of all <math><mi>n</mi></math>-point MHV amplitudes through three loops. Considering the same test for <math><mi>N</mi><mo>=</mo><mn>8</mn></math> 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\u2014which would be automatic at two loops for representation obtained by color-kinematic duality\u2014and gauge invariance\u2014which would follow from unitarity-based methods."
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Published on:
15 March 2019
Publisher:
APS
Published in:
Physical Review D , Volume 99 (2019)
Issue 6
DOI:
https://doi.org/10.1103/PhysRevD.99.066006
arXiv:
1812.11185
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

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