Abstract
The duality between color and kinematics enables the construction of multiloop gravity integrands directly from corresponding gauge-theory integrands. This has led to new nontrivial insights into the structure of gravity theories, including the discovery of enhanced ultraviolet cancellations. To continue to gain deeper understandings and probe these new properties, it is crucial to further improve techniques for constructing multiloop gravity integrands. In this paper, we show by example how one can alleviate difficulties encountered at the multiloop level by relaxing the color-kinematics duality conditions to hold manifestly only on unitarity cuts instead of globally on loop integrands. As an example, we use a minimal ansatz to construct an integrand for the two-loop four-point nonsupersymmetric pure Yang-Mills amplitude in $D$ dimensions that is compatible with these relaxed color-kinematics duality constraints. We then immediately obtain a corresponding gravity integrand through the double-copy procedure. Comments on ultraviolet divergences are also included.
Highlights
The duality between color and kinematics [1,2] offers a practical means for obtaining difficult-to-construct higher-loop scattering amplitudes in gravity theories
The duality between color and kinematics enables the construction of multiloop gravity integrands directly from corresponding gauge-theory integrands
We show by example how one can alleviate difficulties encountered at the multiloop level by relaxing the color-kinematics duality conditions to hold manifestly only on unitarity cuts instead of globally on loop integrands
Summary
The duality between color and kinematics [1,2] offers a practical means for obtaining difficult-to-construct higher-loop scattering amplitudes in gravity theories. Once the duality is manifest in a gauge-theory amplitude, corresponding gravity amplitude integrands are obtained by replacing gauge-theory color factors with dualitysatisfying kinematic numerators This is known as the “double-copy” construction of gravity. Recent work based on twistor string theory and scattering equations offers a new avenue for constructing gravity loop amplitudes that manifest the double-copy structure [16]. A generic problem with using Ansätze to construct kinematic numerators is they may not be general enough This issue is important for state-of-the-art calculations: For example, it has proven difficult to construct integrands for the five-loop four-point amplitude of N 1⁄4 4 super-YangMills theory that manifest BCJ duality between color and kinematics [17].
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