Yangian-type symmetries of non-planar leading singularities

Frassek, Rouven; Meidinger, David

doi:10.48550/arxiv.1603.00088

Cited by 3 publications

(5 citation statements)

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“…This strategy has been pursued in Ref. [23] to find symmetries of leading singularities of nonplanar integrands. Here we will find symmetries of the complete off-shell integrand, up to anomalies introduced by dimensional regularization of infrared singularities, similar to the situation in the planar case.…”

Section: Nonplanar Analog Of Dual Conformal Symmetrymentioning

confidence: 99%

“…The use of dual conformal symmetry also extends to a large class of planar Feynman integrals in even integer dimensions, with an appropriate number of propagators [1,21,22]. This is easiest to implement for planar diagrams where dual conformal symmetry is defined, but as we shall see by opening up nonplanar diagrams into planar diagrams [23], we identify a symmetry that is analogous to dual conformal symmetry.…”

Section: Introductionmentioning

confidence: 99%

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Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector

et al. 2017

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We show that dual conformal symmetry, mainly studied in planar N = 4 super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple observation is that dual conformal transformations preserve unitarity cut conditions for any planar integrals, including those without dual conformal symmetry. Such transformations generate differential equations without raised propagator powers, often with the right hand side of the system proportional to the dimensional regularization parameter ǫ. A nontrivial subgroup of dual conformal transformations, which leaves all external momenta invariant, generates integration-by-parts relations without raised propagator powers, reproducing, in a simpler form, previous results from computational algebraic geometry for several examples with up to two loops and five legs. By opening up the two-loop three-and four-point nonplanar diagrams into planar ones, we find a nonplanar analog of dual conformal symmetry. As for the planar case this is used to generate integration-by-parts relations and differential equations. This implies that the symmetry is tied to the analytic properties of the nonplanar sector of the two-loop four-point amplitude of N = 4 super-Yang-Mills theory.

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Section: Nonplanar Analog Of Dual Conformal Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector

et al. 2017

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“…We can easily recover the original expressions for the amplitudes in (1). For example, if we choose α 1 , α 2 as our integration variables and integrate them against the final delta function in (27), this gives α 1 = 23 /α 3 12 and α 2 = 31 /α 3 12 along with the Jacobian factor 1/α 2 3 12 . One finds that α 3 drops out and using…”

Section: Edge Variables and Perfect Orientationsmentioning

confidence: 99%

“…An important question is how to generalize these ideas beyond planar N = 4 SYM. Although there has been some work on non-planar on-shell diagrams [18,[24][25][26][27], on-shell diagrams for form factors in N = 4 SYM [28], and amplitudes in N < 4 SYM [29], onshell diagrams for gravitational amplitudes have so far not been explored. Since gravity amplitudes are intrinsically non-planar, any new results in this direction may also suggest new techniques for computing non-planar YM amplitudes.…”

Section: Introductionmentioning

confidence: 99%

On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes

Heslop

Lipstein

2016

J. High Energ. Phys.

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We define recursion relations for N = 8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar N = 4 super-Yang-Mills. Although the recursion relations generically give rise to non-planar on-shell diagrams, we show that at tree-level the recursion can be chosen to yield only planar diagrams, the same diagrams occurring in the planar N = 4 theory. This implies non-trivial identities for nonplanar diagrams as well as interesting relations between the N = 4 and N = 8 theories. We show that the on-shell diagrams of N = 8 supergravity obey equivalence relations analogous to those of N = 4 super-Yang-Mills, and we develop a systematic algorithm for reading off Grassmannian integral formulae directly from the on-shell diagrams. We also show that the 1-loop 4-point amplitude of N = 8 supergravity can be obtained from on-shell diagrams.

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“…It is nontrivial that such a representation exists where each integrand is expressed in terms of local diagrams. Some structures of the non-planar sector were also explored at the level of on-shell diagrams [21,22].…”

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confidence: 99%

Dual Conformal Structure Beyond the Planar Limit

et al. 2018

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The planar scattering amplitudes of N = 4 super-Yang-Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four-and five-point amplitudes of N = 4 super-Yang-Mills theory, symmetries analogous to dual conformal invariance exist. A natural conjecture is that this continues to all amplitudes of the theory at any loop order.

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Yangian-type symmetries of non-planar leading singularities

Cited by 3 publications

References 0 publications

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector

On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes

Dual Conformal Structure Beyond the Planar Limit

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