Manifest colour-kinematics duality and double-copy in the string-based formalism

TL;DR

This paper demonstrates a manifest colour-kinematics duality and double-copy construction for multi-particle fields within string-inspired formalisms, providing explicit gravitational currents without gauge fixing.

Contribution

It introduces a new formalism linking multi-particle polarizations to colour-kinematics duality, enabling explicit double-copy gravitational currents in string-based frameworks.

Findings

Derived double-copy gravity Berends-Giele currents.

Explicit construction of Yang-Mills and gravity currents.

Applicable to $oldsymbol{ ext{alpha'}}$-deformed gravity and bi-adjoint scalar models.

Abstract

The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy colour-kinematics duality. In previous work it has been show that this arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and here we show that the tensor product for multi-particle fields arise naturally in the Bern-Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents, and to obtain both the colour-dressed Yang-Mills Berends-Giele currents in the Bern-Carrasco-Johansson gauge and the gravitational Berends-Giele currents explicitly. An attractive feature of our formalism is that it never becomes necessary to determine gauge transformation terms. Our double-copy prescription can also be applied to other cases, and to make this point we derive the double-copy perturbiners for $\alpha'$-deformed gravity and the bi-adjoint scalar model.