Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

TL;DR

This paper demonstrates the color-kinematics duality in nonsupersymmetric pure Yang-Mills theory at one and two loops, enabling the construction of gravity amplitudes from gauge theory in various dimensions.

Contribution

It constructs explicit duality-satisfying amplitude representations at one and two loops for pure Yang-Mills, extending the duality beyond supersymmetric theories.

Findings

Manifest duality form for one-loop four-point amplitude in any dimension.

Duality-satisfying two-loop four-point amplitude with specific helicities.

Explicit gravity integrands derived from gauge theory amplitudes.

Abstract

We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.