Kinematic numerators from the worldsheet: cubic trees from labelled trees

He, Song; Hou, Lianping; Tian, Jintian; Zhang, Yong

doi:10.1007/jhep08(2021)118

Cited by 24 publications

(15 citation statements)

References 63 publications

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“…There has been considerable effort dedicated to the explicit evaluation of BCJ numerators [8,49,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68]. However, a completely general, closed-form, analytic expression has proven elusive.…”

Section: Analytic Formulas For Amplitudesmentioning

confidence: 99%

Covariant color-kinematics duality

Cheung

Mangan

2021

J. High Energ. Phys.

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We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory.For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D2. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background.Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

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Section: Analytic Formulas For Amplitudesmentioning

confidence: 99%

Covariant color-kinematics duality

Cheung

Mangan

2021

J. High Energ. Phys.

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“…Formulas related to (3.4) appear in the discussion of hyperplane arrangements in [43]. The functions, (3.3), associated to a spanning tree G are studied in [27], with interesting applications to CHY formulas.…”

Section: Scattering Equations Identitiesmentioning

confidence: 99%

“…Einstein gravity, and Dirac-Born-Infeld theory, which are the gravity theories associated to YM and NLSM, respectively. There have been several previous studies that obtain formulas of this kind from CHY integrals, including [5,21,27]. The approach taken here is novel, and combines applications of the matrix tree theorem with the identities proved in Section 3.…”

Section: Gauge and Gravity Tree Amplitudes In Bcj Formmentioning

confidence: 99%

The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes

Frost

2021

SIGMA

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We study the Kawai-Lewellen-Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise when studying rational functions on M 0,n , and prove identities that allow for arbitrary rational functions to be expanded in any given basis. Via the Cachazo-He-Yuan formulas for, these identities also lead to new formulas for gauge and gravity tree amplitudes, including formulas for so-called Bern-Carrasco-Johansson numerators, in the case of non-linear sigma model and maximal-helicity-violating Yang-Mills amplitudes.

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“…Note that the "quotient" theory is again universal: for gauge-theory expansions I/II = YM, and for EFT ones, I/II = NLSM. Such expansions thus provide a systematic way for extracting kinematic numerators needed in all these theories, and this way of extracting them was originally found using CHY formulas in [34,36,42] (see also [43,44]) and automatized in [45,46]. Different choices of reference particles lead to different recursive expansions and BCJ numerators, but all of them are equivalent.…”

Section: Double and Recursive Expansions And Double Copymentioning

confidence: 99%

Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles

Dong,

He,

Hou

2021

Preprint

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Tree-level scattering amplitudes for gravitons, gluons and Goldstone particles in any dimensions are strongly constrained by basic principles, and they are intimately related to each other via various relations. We study two types of "universal expansions" with respect to gauge bosons and Goldstone bosons: the former express tree amplitudes in Einstein gravity (Yang-Mills) as linear combinations of single-trace Einstein-Yang-Mills (Yang-Mills-φ 3 ) amplitudes with coefficients given by Lorentz products of polarizations and momenta; the latter express tree amplitudes in non-linear sigma model, (Dirac-)Born-Infeld and a special Galileon theory, as linear combinations of singletrace mixed amplitudes with particles of lower "degree of Adler's zero" and coefficients given by products of Mandelstam variables. We trace the origin of gauge-theory expansions to the powerful uniqueness theorem based on gauge invariance, and expansions in effective field theories can be derived from gauge-theory ones via a special dimension reduction.

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Kinematic numerators from the worldsheet: cubic trees from labelled trees

Cited by 24 publications

References 63 publications

Covariant color-kinematics duality

Covariant color-kinematics duality

The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes

Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles

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