Gluons and gravitons at one loop from ambitwistor strings

TL;DR

This paper derives explicit one-loop scattering amplitude formulas for gauge theory and gravity using ambitwistor string theory, revealing color-kinematics duality and double-copy relations in a new, simplified integrand form.

Contribution

It introduces a novel representation of one-loop integrands with a single quadratic propagator, derived from ambitwistor string theory, applicable to various dimensions and theories.

Findings

Explicit one-loop integrand formulas for gauge and gravity theories.

Validation of gauge invariance and matching with known results.

Representation simplifies checks compared to traditional Feynman approaches.

Abstract

We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions based on the scattering equations that were recently derived from ambitwistor string theory. We turn these expressions into explicit formulae depending only on the loop momentum, the external momenta and the external polarisations. These formulae are valid in any number of spacetime dimensions for pure Yang-Mills theory (gluon) and its natural double copy, NS-NS gravity (graviton, dilaton, B-field), and we also present formulae in four spacetime dimensions for pure gravity (graviton). We perform several tests of our results, such as checking gauge invariance and directly matching our four-particle formulae to previously known expressions. While these tests would be elaborate in a Feynman-type representation of the loop integrand, they become straightforward in the representation we use.