Double-Copy Constructions and Unitarity Cuts

TL;DR

This paper advances multiloop gravity integrand construction by relaxing color-kinematics duality conditions to unitarity cuts, demonstrated through a two-loop Yang-Mills example, facilitating gravity integrand derivation and insights into ultraviolet behavior.

Contribution

It introduces a method to construct gravity integrands by relaxing duality conditions to unitarity cuts, simplifying multiloop calculations and enabling new insights into ultraviolet properties.

Findings

Constructed a two-loop four-point Yang-Mills integrand compatible with relaxed duality.

Derived a gravity integrand via double-copy from the gauge-theory integrand.

Discussed implications for ultraviolet divergences in gravity theories.

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.