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Loop-level KLT, BCJ and EYM amplitude relations

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He,  Song
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Schlotterer,  Oliver
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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1612.00417.pdf
(Preprint), 171KB

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Citation

He, S., & Schlotterer, O. (in preparation). Loop-level KLT, BCJ and EYM amplitude relations.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002C-59BE-2
Abstract
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. Finally, we briefly report on preliminary two-loop evidence that the KLT formula can be extended to any loop order.