String-inspired BCJ numerators for one-loop MHV amplitudes

He, Song; Monteiro, Ricardo; Schlotterer, Oliver

doi:10.1007/jhep01(2016)171

Cited by 101 publications

(113 citation statements)

References 135 publications

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“…with the standard super-momentum conserving delta function δ 8 (Q) [29], and the n-point generalization can be straightforwardly extracted from [30]. We have checked up to n=10 explicitly, and expect to have a allmultiplicity proof, that our one-loop KLT formula (7) reproduces the MHV supergravity integrands of [30].…”

Section: B 3pt Half-maximalmentioning

confidence: 86%

“…We have checked up to n=10 explicitly, and expect to have a allmultiplicity proof, that our one-loop KLT formula (7) reproduces the MHV supergravity integrands of [30].…”

Section: B 3pt Half-maximalmentioning

confidence: 91%

“…MHV maximal: BCJ numerators for one-loop MHV amplitudes in N = 4 SYM have been given at all multiplicities [30] in terms of…”

Section: B 3pt Half-maximalmentioning

confidence: 99%

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New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

Schlotterer

2017

Phys. Rev. Lett.

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In this letter, we extend the tree-level Kawai-Lewellen-Tye (KLT) and Bern-Carrasco-Johansson (BCJ) amplitude relations to loop integrands of gauge theory and gravity. By rearranging the propagators of gauge and gravity loop integrands, we propose the first manifestly gauge-and diffeomorphism invariant formulation of their double-copy relations. The one-loop KLT formula expresses gravity integrands in terms of more basic gauge invariant building blocks for gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop analogue of the BCJ relations, and both KLT and BCJ relations are universal to bosons and fermions in any number of spacetime dimensions and independent on the amount of supersymmetry. Also, one-loop integrands of Einstein-Yang-Mills (EYM) theory are related to partial integrands of pure gauge theories.

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Section: B 3pt Half-maximalmentioning

confidence: 86%

“…We have checked up to n=10 explicitly, and expect to have a allmultiplicity proof, that our one-loop KLT formula (7) reproduces the MHV supergravity integrands of [30].…”

Section: B 3pt Half-maximalmentioning

confidence: 91%

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New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

Schlotterer

2017

Phys. Rev. Lett.

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“…String theory continues to provide key insights probing the color-kinematics duality and its associated representation of the double-copy construction: from the powerful proof [11,12] of the (n−3)!-basis of Yang-Mills tree amplitudes as the low-energy limit of the related string monodromy relations, 7 to the elegant construction of explicit local treelevel numerators [57][58][59], to the construction of string-inspired BCJ numerators [60][61][62] at loop level. 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.…”

Section: Jhep06(2017)093mentioning

confidence: 99%

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

Carrasco

Mafra

Schlotterer

2017

J. High Energ. Phys.

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144

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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“…7 Moreover, there has been recent progress in formulating loop amplitudes using CHY formulas (e.g. [50][51][52][53]) and it will be a natural extension to study soft and collinear limits at the loop level. Finally, we have studied only a few EFTs under the collinear limit and it would definitely be a very important direction to further understand the space of EFTs using soft and collinear limits.…”

Section: Jhep02(2017)038mentioning

confidence: 99%

Collinear limits beyond the leading order from the scattering equations

Nandan¹,

Plefka²,

Wormsbecher³

2017

J. High Energ. Phys.

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The structure of tree-level scattering amplitudes for collinear massless bosons is studied beyond their leading splitting function behavior. These near-collinear limits at sub-leading order are best studied using the Cachazo-He-Yuan (CHY) formulation of the S-matrix based on the scattering equations. We compute the collinear limits for gluons, gravitons and scalars. It is shown that the CHY integrand for an n-particle gluon scattering amplitude in the collinear limit at sub-leading order is expressed as a convolution of an (n − 1)-particle gluon integrand and a collinear kernel integrand, which is universal. Our representation is shown to obey recently proposed amplitude relations in which the collinear gluons of same helicity are replaced by a single graviton. Finally, we extend our analysis to effective field theories and study the collinear limit of the non-linear sigma model, EinsteinMaxwell-Scalar and Yang-Mills-Scalar theory.

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String-inspired BCJ numerators for one-loop MHV amplitudes

Cited by 101 publications

References 135 publications

New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

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

Collinear limits beyond the leading order from the scattering equations

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