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

## TL;DR

This paper presents a systematic method to construct one-loop amplitude representations in gauge theories and gravity that explicitly manifest the Bern-Carrasco-Johansson duality, applicable across various supersymmetric theories and dimensions.

## Contribution

It introduces a new procedure to realize BCJ duality in one-loop amplitudes using the CHY formalism, independent of spacetime dimensions and supersymmetry levels.

## Key findings

- Explicit amplitude representations for various supersymmetric gauge theories.
- Derivation of the one-loop Kawai-Lewellen-Tye formula for gravitational amplitudes.
- Manifestation of supersymmetry cancellations and power counting in loop integrands.

## Abstract

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. The setup is used to derive the one-loop version of the Kawai-Lewellen-Tye formula for the loop integrands of gravitational amplitudes.

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Source: https://tomesphere.com/paper/1706.00640