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New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

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arxiv 1612.00417 v2 pith:LOJSGUWJ submitted 2016-12-01 hep-th

Song He , Oliver Schlotterer This is my paper · ORCID
classification hep-th
keywords integrandsrelationsgaugegravityloopone-loopamplitudesgauge-theory
verification ladder T0 review T1 audit T2 compute T3 formal
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In this letter, we extend the tree-level Kawai--Lewellen--Tye (KLT) and Bern--Carrasco--Johansson (BCJ) amplitude relations to loop integrands of gauge theory and gravity. By rearranging the propagators of gauge and gravity loop integrands, we propose the first manifestly gauge- and diffeomorphism invariant formulation of their double-copy relations. The one-loop KLT formula expresses gravity integrands in terms of more basic gauge invariant building blocks for gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop analogue of the BCJ relations, and both KLT and BCJ relations are universal to bosons and fermions in any number of spacetime dimensions and independent on the amount of supersymmetry. Also, one-loop integrands of Einstein--Yang--Mills (EYM) theory are related to partial integrands of pure gauge theories.

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Cited by 4 Pith papers

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

  1. Gleaning gravitational amplitudes -- a double copy for canceling dilatons

    hep-th 2025-01 conditional novelty 7.0 of 10

    An asymmetric double copy with a ghost-like sqrt-dilaton cancels dilaton contaminations in tree-level GR amplitudes with massive scalars up to six points, leaving a residual bubble ambiguity at one loop.

  2. An adaptive inverse-problem framework for one-loop five-gluon BCJ numerators

    hep-th 2026-07 conditional novelty 6.0 of 10

    The complete 207-dimensional family of one-loop five-gluon BCJ numerator coefficients is reconstructed exactly, and every direction in that family is shown to be invisible to the specified color-ring observable.

  3. On one-loop amplitudes in gauge theories

    hep-th 2024-12 conditional novelty 6.0 of 10

    A universal expansion expresses one-loop n-gluon amplitudes in general gauge theories as scalar-loop integrands dressed by matter-dependent gauge-invariant traces.

  4. Expansion formula of one-loop Einstein-Yang-Mills integrand

    hep-th 2025-12 conditional novelty 5.0 of 10

    Gluon-loop one-loop EYM integrands expand into quadratic-propagator one-loop YM integrands with the same coefficients as the YMS expansion, provided the forward-limit expansion coefficients obey the one-loop consisten...

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