Explicit BCJ numerators of nonlinear simga model

Du, Yi-Jian; Fu, Chih-Hao

doi:10.1007/jhep09(2016)174

Cited by 72 publications

(90 citation statements)

References 65 publications

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“…Along the way we provide a nice recursive form of the KLT matrix S[·|·] 1 , inspired by ref. [19], and propose a strikingly simple form for all-multiplicity n = 2k NLSM color-kinematic satisfying master numerators…”

Section: Jhep06(2017)093mentioning

confidence: 99%

“…The fact that the BCJ-duality also applies to the NLSM [40], can now be appreciated either as a consequence of the BCJ relations satisfied [3] by Z-theory as in (1.3), or as a requirement for the NLSM to be able to participate in Z-theory's construction of the open superstring. Following the recent result of Du and Fu [19] who present an elegant closed-form construction of local color-kinematics satisfying numerators in the NLSM, we will discuss its applicability to all orders in α ′ . 6 Established to some finite multiplicity at tree-level in [5], but later proven via BCFW and the KLT relations in [38].…”

Section: Jhep06(2017)093mentioning

confidence: 99%

“…One should expect that if such a local representation is always possible for a theory then there should be a closed form for local masters. 17 Indeed, the authors of [19] present such a closed-form construction for the NLSM, making the key-insight that the symmetric (n − 2)! × (n − 2)!…”

Section: Color-kinematic Satisfying Numeratorsmentioning

confidence: 99%

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Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

Carrasco

Mafra

Schlotterer

2017

J. High Energ. Phys.

140

232

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In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory -the collection of putative scalar effective field theories encoding all the α ′ -expansion of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of α ′ in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The amplitude relations due to Kleiss-Kuijf as well as Bern, Johansson and one of the current authors obeyed by Z-theory amplitudes thereby apply to all α ′ -corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kinematic numerators obey the duality between color and kinematics to all orders in α ′ .

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Section: Jhep06(2017)093mentioning

confidence: 99%

Section: Jhep06(2017)093mentioning

confidence: 99%

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Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

Carrasco

Mafra

Schlotterer

2017

J. High Energ. Phys.

140

232

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“…In [26] and [27], two different constructions are proposed from the off-shell extension of BCJ relation in NLSM and Abelian Z-theory respectively:…”

Section: The Equivalence To Other Constructionsmentioning

confidence: 99%

“…The convention for S follows the paper [27]. In the DF construction, ρ presents a certain subset of permutations (see [26]). Noticing that only amplitudes with even number external particles in NLSM are nonzero, so that the n/2 in the CMS construction must be an integer.…”

Section: The Equivalence To Other Constructionsmentioning

confidence: 99%

BCJ numerators from reduced Pfaffian

Teng

2017

J. High Energ. Phys.

Self Cite

103

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By expanding the reduced Pfaffian in the tree level Cachazo-He-Yuan (CHY) integrands for Yang-Mills (YM) and nonlinear sigma model (NLSM), we can get the BernCarrasco-Johansson (BCJ) numerators in Del Duca-Dixon-Maltoni (DDM) form for arbitrary number of particles in any spacetime dimensions. In this work, we give a set of very straightforward graphic rules based on spanning trees for a direct evaluation of the BCJ numerators for YM and NLSM. Such rules can be derived from the Laplace expansion of the corresponding reduced Pfaffian. For YM, the each one of the (n − 2)! DDM form BCJ numerators contains exactly (n − 1)! terms, corresponding to the increasing trees with respect to the color order. For NLSM, the number of nonzero numerators is at most (n − 2)! − (n − 3)!, less than those of several previous constructions.

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Double Copy from Homotopy Algebras

Borsten

Kim

Jurčo

et al. 2021

Fortschritte der Physik

100

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We show that the BRST Lagrangian double copy construction of N=0 supergravity as the ‘square’ of Yang–Mills theory finds a natural interpretation in terms of homotopy algebras. We significantly expand on our previous work arguing the validity of the double copy at the loop level, and we give a detailed derivation of the double‐copied Lagrangian and BRST operator. Our constructions are very general and can be applied to a vast set of examples.

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Explicit BCJ numerators of nonlinear simga model

Cited by 72 publications

References 65 publications

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

Abelian Z-theory: NLSM amplitudes and α ′ -corrections from the open string

BCJ numerators from reduced Pfaffian

Double Copy from Homotopy Algebras

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