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High Energy Physics - Theory, hep-th
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.
