Local BCJ numerators for ten-dimensional SYM at one loop

Bridges, Elliot; Mafra, Carlos R.

doi:10.1007/jhep07(2021)031

Cited by 20 publications

(22 citation statements)

References 61 publications

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“…As mentioned, our tree-level result can be uplifted to one loop via forward limit with a pair of momenta in higher dimensions (see [22,23]), which gives integrand with propagators linear in loop momentum. It would be highly desirable to find a systematic method for extracting kinematic numerators efficiently at loop level with quadratic propagators (see [64,65] and references therein). Finally, our original motivation for introducing Cayley functions is due to their geometric interpretation, e.g.…”

Section: Jhep08(2021)118 4 Outlookmentioning

confidence: 99%

Kinematic numerators from the worldsheet: cubic trees from labelled trees

Hou

Tian

et al. 2021

J. High Energ. Phys.

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In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with kinematic numerators automatically satisfying Jacobi-identities, once any half-integrand on the worldsheet is reduced to logarithmic functions. We review a natural class of worldsheet functions called “Cayley functions”, which are in one-to-one correspondence with labelled trees, and natural expansions of known half-integrands onto them with coefficients that are particularly compact building blocks of kinematic numerators. We present a general formula expressing kinematic numerators of all cubic trees as linear combinations of coefficients of labelled trees, which satisfy Jacobi identities by construction and include the usual combinations in terms of master numerators as a special case. Our results provide an efficient algorithm, which is implemented in a Mathematica package, for computing all tree amplitudes in theories including non-linear sigma model, special Galileon, Yang-Mills-scalar, Einstein-Yang-Mills and Dirac-Born-Infeld.

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Section: Jhep08(2021)118 4 Outlookmentioning

confidence: 99%

Kinematic numerators from the worldsheet: cubic trees from labelled trees

Hou

Tian

et al. 2021

J. High Energ. Phys.

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“…Particularly interesting features can be expected at six points: first, our method qualifies for explicit investigations of αcorrections to the one-loop hexagon anomaly of ten-dimensional super-Yang-Mills [191,192] and its cancellation for type-I superstrings [193,194]. Second, one-loop six-point amplitudes in field theory pose additional challenges [122,123] in manifesting the color-kinematics duality and double copy as compared to ≤ 5 points, at least in D = 10 dimensions and through quadratic Feynman propagators [21]. More specifically, while a four-dimensional construction have been understood for some time [195], it remains to iron out details of the double copy for the SYM loop integrand recently obtained in [123].…”

Section: Discussionmentioning

confidence: 97%

“…Second, one-loop six-point amplitudes in field theory pose additional challenges [122,123] in manifesting the color-kinematics duality and double copy as compared to ≤ 5 points, at least in D = 10 dimensions and through quadratic Feynman propagators [21]. More specifically, while a four-dimensional construction have been understood for some time [195], it remains to iron out details of the double copy for the SYM loop integrand recently obtained in [123].…”

Section: Discussionmentioning

confidence: 99%

“…For maximally supersymmetric SYM with 16 supercharges, the numerators N +|12...n|− ( ) in (2.8) are well-known to be degree-(n−4) polynomials in the loop momentum. Manifestly supersymmetric expressions in pure-spinor superspace [120,121] can be found in [122,123]. For external gluons, the four-and five-point examples to be discussed in section 4 are expressible in terms of the standard t 8 -tensor contracting polarization vectors.…”

Section: One-loop Amplitudes From Ambitwistor Stringsmentioning

confidence: 99%

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One-loop matrix elements of effective superstring interactions: α′-expanding loop integrands

Edison

Guillen

Johansson

et al. 2021

J. High Energ. Phys.

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In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D2kFn and D2kRn in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α′. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α′. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

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“…Amplitude relations have been studied from many complementary perspectives, such as string theory, scattering equations and positive geometry [4,5,[143][144][145]. By now there exist many direct methods for the construction of BCJ numerators [51,[146][147][148][149][150][151][152][153][154][155][156][157][158][159]. However, to gain a complete understanding of this topic, direct exploration of the structure of the underlying kinematic algebra is necessary.…”

Section: Introductionmentioning

confidence: 99%

Off-Shell Color-Kinematics Duality for Chern-Simons

Ben-Shahar¹,

Johansson²

2021

Preprint

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Many gauge theories possess a hidden duality between color and kinematics in their on-shell scattering amplitudes. An open problem is to formulate an off-shell realization of the duality, thus manifesting a kinematic algebra. We show that 3D Chern-Simons (CS) theory in Lorenz gauge obeys off-shell color-kinematics duality. This holds both for the gauge field and the BRST ghosts, and the duality is manifest in the Feynman rules. A kinematic algebra can be formulated through a second-order differential operator (Poisson bracket) acting on the off-shell fields, and it corresponds to 3D diffeomorphisms generated by functions in Lorenz gauge. We consider several admissible double-copy constructions of CS theory with Yang-Mills theory, a higher-derivative (DF ) 2 gauge theory, or CS theory itself. To obtain non-vanishing amplitudes, we deform pure CS theory by including the maximum amount of adjoint matter that respects the on-shell duality. This gives a new formulation of an N = 4 CS-matter theory, with fields of unusual statistics. We argue that the color-stripped tree amplitudes of this theory are equivalent to those of the Gaiotto-Witten N = 4 CS theory with bi-fundamental matter. We further show that the double copy of the N = 4 CS theory with itself corresponds to maximally supersymmetric N = 8 Dirac-Born-Infeld theory.

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Local BCJ numerators for ten-dimensional SYM at one loop

Cited by 20 publications

References 61 publications

Kinematic numerators from the worldsheet: cubic trees from labelled trees

Kinematic numerators from the worldsheet: cubic trees from labelled trees

One-loop matrix elements of effective superstring interactions: α′-expanding loop integrands

Off-Shell Color-Kinematics Duality for Chern-Simons

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