New BCJ representations for one-loop amplitudes in gauge theories and gravity

Understand

We explain a procedure to manifest the Bern-Carrasco-Johansson duality between color and kinematics in $n$-point one-loop amplitudes of a variety of supersymmetric gauge theories.

• Explicit amplitude representations are constructed through a systematic reorganization of the integrands in the Cachazo-He-Yuan formalism.
• Our construction holds for any nonzero number of supersymmetries and does not depend on the number of spacetime dimensions.
• The cancellations from supersymmetry multiplets in the loop as well as the resulting power counting of loop momenta is manifested along the lines of the corresponding superstring computations.