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Amplitudes at Infinity

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arxiv 1812.11185 v1 pith:MUYYVCPQ submitted 2018-12-28 hep-th

Jacob L. Bourjaily , Enrico Herrmann , Jaroslav Trnka This is my paper · ORCID
classification hep-th
keywords amplitudesinfinityloopsmathcalpolessupersymmetrictheoryabsence
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We investigate the asymptotically large loop-momentum behavior of multi-loop amplitudes in maximally supersymmetric 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 MHV amplitudes through three loops. Considering the same test for $\mathcal{N}=8$ supergravity leads us to discover that this theory does support non-vanishing 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 in a representation obtained by color-kinematic duality---and gauge invariance---which would follow from unitarity-based methods.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Smooth Splitting and Zeros from On-Shell Recursion

    hep-th 2025-05 conditional novelty 8.0 of 10

    Hidden zeros and smooth splitting in Tr phi^3, NLSM, YMS, and the special Galileon are shown to follow from on-shell recursion under improved UV falloff, yielding generalized, triple, and 4d helicity zeros.

  2. Gravity loop integrands from the ultraviolet

    hep-th 2019-09 conditional novelty 7.0 of 10

    Four-dimensional N=8 supergravity loop integrands scale one power better at infinity than general-D power-counting predicts, and this homogeneous scaling combined with BCFW behavior uniquely fixes the integrand throug...

  3. UV considerations on scattering amplitudes in a web of theories

    hep-th 2019-08 conditional novelty 6.0 of 10

    Tree-level amplitudes in a web of effective field theories are uniquely fixed by locality plus novel single-hard UV scaling constraints, with unitarity emerging in many cases.

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