Abstract
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 selfdualtype vertex which is associated to each solution of those equations. We also identify an extension of the antiselfdual 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.
Original language  English 

Article number  110 
Journal  Journal of High Energy Physics 
Volume  14 
Issue number  03 
DOIs  
Publication status  Published  24 Mar 2014 
Keywords
 Scattering Amplitudes
 Duality in Gauge Field Theories
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Donal O'Connell
 School of Physics and Astronomy  Personal Chair of Theoretical Particle Physics
Person: Academic: Research Active