Dual-color decompositions at one-loop level in Yang-Mills theory

Abstract

In this work we extend two dual color decompositions of Yang-Mills amplitude to one-loop level. Starting from double-copy expression we translate the Yang-Mills integrand into the dual Del Duca-Dixon-Maltoni formulation and subsequently to the dual color-ordered formula. The dual trace factors are obtained after simultaneously solving the one-loop Kleiss-Kuijf relations, the reflection relation, and the relation that expresses the kinematic factors in the dual Del Duca-Dixon-Maltoni form.

Monopoles, shockwaves and the classical double copy

“…[48] left as merely speculative the suggestion that the biadjoint monopoles of eqs. (15,17) are related to the Wu-Yang monopole. Our aim here is to examine this systematically, and the starting point will be the above-mentioned fact that shockwave solutions are known to double copy.…”

The Newman-Penrose map and the classical double copy

“…where V is a real function and Φ,Φ are complex conjugates. 9,10 The full metric is determined completely once V and Φ are specified. Although V satisfies its own potentially interesting set of constraints (see [40]), from now on we focus on the complex function Φ, which will turn out to be harmonic with respect to the background metric and so an intuitive starting point for mapping gravitational solutions to self-dual gauge fields.…”

“…The gauge-gravity double copy relates perturbative scattering amplitudes in non-abelian gauge theory to amplitudes of a gravitational theory by replacing color factors with additional kinematic information [1][2][3][4]. Originally formulated to relate open and closed string amplitudes via the KLT (Kawai-Lewellen-Tye) relations [5], this subject has seen great progress in recent years: color-kinematic duality and the double copy have been proven at JHEP12(2020)121 tree level [2], appear to hold at loop level [3,[6][7][8][9][10], and are widely believed to hold to all orders in perturbation theory [11,12]. The power of the double copy in relating gravity to gauge theories provides new computational tools that can, for instance, be leveraged to simplify and improve calculations of black hole merger in-spirals [13][14][15][16].…”

Note on symmetric BCJ numerator

“…f x n−3 σ n−2 n and A(1, σ, n) are color-ordered Yang-Mills amplitudes. The BCJ dual of the original trace form of color decomposition was studied in [22,[24][25][26].…”

“…The apparently symmetrical structure also suggests mirror versions of the existing color decomposition formulations. In particular that studies of the BCJ duals of the Del Duca-Dixon-Maltoni(DDM) form [20] and the original trace form of color decomposition formulations can be found in [11,[21][22][23][24][25][26]. For example at tree-level, the full Yang-Mills amplitude were shown to be expressible in…”