Yangian-type symmetries of non-planar leading singularities

Frassek, Rouven; Meidinger, David

doi:10.1007/jhep05(2016)110

Cited by 13 publications

(21 citation statements)

References 36 publications

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“…The corresponding double-row monodromy is the same as for the line solution, cf. (30), but the identification of the rapidities with the inhomogeneities changes according to (23). As a consequence of the boundary Yang-Baxter equation (8) the boundary-line invariant in (36) satisfies…”

Section: Boundary-line Invariantmentioning

confidence: 99%

Boundary perimeter Bethe ansatz

Frassek¹

2017

J. Phys. A: Math. Theor.

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We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.

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Section: Boundary-line Invariantmentioning

confidence: 99%

Boundary perimeter Bethe ansatz

Frassek¹

2017

J. Phys. A: Math. Theor.

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“…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%

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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“…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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Yangian-type symmetries of non-planar leading singularities

Cited by 13 publications

References 36 publications

Boundary perimeter Bethe ansatz

Boundary perimeter Bethe ansatz

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

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

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