Algebras for amplitudes

Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Monteiro, Ricardo; O’Connell, Donal

doi:10.1007/jhep06(2012)061

Cited by 147 publications

(185 citation statements)

References 80 publications

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“…Both the color-kinematics duality and the double copy are well understood at tree level [12,21,[26][27][28][29][30][31]. The recently developed formalism of the scattering equations has JHEP01(2016)171 brought a new insight into these structures [32][33][34][35][36][37].…”

Section: Bcj Duality and Double Copymentioning

confidence: 99%

String-inspired BCJ numerators for one-loop MHV amplitudes

Monteiro

Schlotterer

2016

J. High Energ. Phys.

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We find simple expressions for the kinematic numerators of one-loop MHV amplitudes in maximally supersymmetric Yang-Mills theory and supergravity, at any multiplicity. The gauge-theory numerators satisfy the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics, so that the gravity numerators are simply the square of the gauge-theory ones. The duality holds because the numerators can be written in terms of structure constants of a kinematic algebra, which is familiar from the BCJ organization of self-dual gauge theory and gravity. The close connection that we find between one-loop amplitudes in the self-dual case and in the maximally supersymmetric case is reminiscent of the dimension-shifting formula. The starting point for arriving at our expressions is the dimensional reduction of ten-dimensional amplitudes obtained in the field-theory limit of open superstrings.

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Section: Bcj Duality and Double Copymentioning

confidence: 99%

String-inspired BCJ numerators for one-loop MHV amplitudes

Monteiro

Schlotterer

2016

J. High Energ. Phys.

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101

104

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“…In general, such choice of numerators is non-unique, but non-trivial to find. By now, various algorithms have been described for finding BCJ numerators; see, for example, [23,[31][32][33]37]. We shall discuss below how the scattering equations are naturally associated with a certain set of numerators.…”

Section: Jhep03(2014)110mentioning

confidence: 99%

“…We see this result as a direct consequence of the fact, proven in [30], that the Parke-Taylor factors arising from each solution of the scattering equations (to be reviewed next) satisfy the so-called BCJ relations. Explicit constructions to invert the linear problem and generate BCJ numerators for amplitudes satisfying the BCJ relations were presented in [31][32][33]. In this work, we provide a canonical set of BCJ numerators which can be constructed directly from the vertex configuration of a trivalent graph, based on algebraic structures naturally associated to the scattering equations.…”

Section: Introductionmentioning

confidence: 99%

The kinematic algebras from the scattering equations

Monteiro

O’Connell

2014

J. High Energ. Phys.

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104

119

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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.

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“…An explicit construction was given by Mafra, Schlotterer and Stieberger using the pure spinor language [34]. Alternatively, it was shown that the kinematic factors can be interpreted in terms of diffeomorphism algebra [23,[35][36][37]. In a series of recent papers [38][39][40] another interesting construction was provided by Cachazo, He and Yuan (CHY) using the solutions to the scattering equations.…”

Section: Jhep08(2014)098mentioning

confidence: 99%

“…Instead of attempting to decipher the analytic structure responsible for the possible algebraic behavior, another line of thoughts is to solve the kinematic numerators reversely in terms of scattering amplitudes, and indeed, it was discussed in [36,41] that such expression for the numerators can always be derived in suitable basis. A technical issue lies with this approach is that because of the complexity involved, along with the ambiguity introduced by generalized gauge invariance, it is practically difficult to write down an analytic expression for generic numerator.…”

Section: Jhep08(2014)098mentioning

confidence: 99%