The construction of dual-trace factor in Yang-Mills theory

102

119

We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant.

Section: Jhep03(2014)110mentioning

confidence: 99%

The kinematic algebras from the scattering equations

Monteiro

O’Connell

2014

102

119

“…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].…”

Section: Jhep08(2014)098mentioning

confidence: 99%

“…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…”

Section: Introductionmentioning

confidence: 99%

Note on symmetric BCJ numerator

Feng

2014

Self Cite

“…Based on the existence of a dual DDM form, the dual trace form was conjectured by Bern and Dennen in [38] with explicit constructions given for the first few lower-point amplitudes. In addition two constructions of the dual trace form was discussed in [40] and [41].…”

Section: Jhep06(2014)157mentioning

confidence: 99%

“…To go from dual DDM form to dual trace-form, we need to find a way to rewrite basis kinematic numerators n α into a linear combination of analogues of "single trace" and "double trace" n trace as what was done at tree-level [38,40,41]. However note that, as in the tree-level case, the number of n trace is much larger than n α , thus extra relations need to be manually imposed in order to solve n trace in terms of n α .…”

Section: Jhep06(2014)157mentioning

confidence: 99%

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

Feng

2014

Self Cite

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.