Correlators with sℓ 2 Yangian symmetry

Fuksa, J.; Kirschner, R.

doi:10.1016/j.nuclphysb.2016.10.019

Cited by 7 publications

(18 citation statements)

References 44 publications

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“…In [26] the eigenvalue problem (2.4) for a non-compact spin chain with Jordan-Schwinger representations of the algebra sl(N ) was studied, and the R-operator method for the superconformal algebra gl(4|4) was investigated in [27][28][29][30][31] to construct tree-level scattering amplitudes in N = 4 SYM, as well as in ABJM theory [32]. The R-operator method of [27] was also applied to construct form factors of composite operators [33,34], the form factors of Wilson lines [35], the kernels of QCD parton evolutions [36], amplituhedron volume functions [37], and splitting amplitudes [38].…”

Section: Yangian Invariants and Monodromy Matrixmentioning

confidence: 99%

Yangian symmetry for bi-scalar loop amplitudes

Chicherin

Казаков

Loebbert

et al. 2018

J. High Energ. Phys.

137

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We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of γ-twisted weakly coupled N = 4 SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.This paper is dedicated to the memory of L.D.Faddeev.

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Section: Yangian Invariants and Monodromy Matrixmentioning

confidence: 99%

Yangian symmetry for bi-scalar loop amplitudes

Chicherin

Казаков

Loebbert

et al. 2018

J. High Energ. Phys.

137

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“…In this section we shall present an alternative derivation of the splitting probabilities for tensorgluons postulating the s 4 Yangian symmetry of the scattering amplitudes of the tensorgluons [18,19,22,21,20,23,24,26]. As we shall demonstrate, the splitting amplitudes calculated within the Yangian symmetry approach coincide with (2.14), (2.15) and…”

Section: Yangian Symmetry Of Parton Splitting Amplitudesmentioning

confidence: 74%

“…In the next section we shall consider the amplitudes which are the solution of the s 2 version of Yangian symmetry (3.20) obtained in [26]. These amplitudes represent a longitudinal, two-dimensional reduction [12] of the four-dimensional s 4 symmetric amplitudes and, as we shall see, the alternative derivation of the splitting probabilities will coincide with the one presented above but has the advantage to represent the results in a more symmetric form.…”

Section: Susy Symmetry Of the Splitting Amplitudesmentioning

confidence: 96%

“…hint to the high symmetry of the generalised Yang-Mills theory amplitudes reminiscent to the symmetries discovered in Yang-Mills theory [18,19,21,20,22,23,24,26]. This is a surprising and encouraging result because such a high symmetry was not explicitly implemented into the initial formulation [1,5,6].…”

Section: Yangian Symmetry Of Parton Splitting Amplitudesmentioning

confidence: 98%

“…The expressions for the parton splitting probabilities given in sect. (3.20), as explained in [26]. The explicit form of the L matrix (in the case…”

Section: S 2 Symmetries Of the Splitting Amplitudesmentioning

confidence: 99%

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Yangian and SUSY symmetry of high spin parton splitting amplitudes in generalised Yang–Mills theory

Kirschner

Savvidy

2017

Mod. Phys. Lett. A

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We have calculated the high spin parton splitting amplitudes postulating the Yangian symmetry of the scattering amplitudes for tensorgluons. The resulting splitting amplitudes coincide with the earlier calculations, which were based on the BCFW recursion relations.The resulting formula unifies all known splitting probabilities found earlier in gauge field theories. It describes splitting probabilities for integer and half-integer spin particles.We also checked that the splitting probabilities fulfil generalised Kounnas-Ross N = 1 supersymmetry relations hinting to the fact that the underlying theory can be formulated in an explicit supersymmetric manner.

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Symmetry properties of Wilson loops with a Lagrangian insertion

Chicherin

Henn

2022

J. High Energ. Phys.

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Null Wilson loops in $$ \mathcal{N} $$ N = 4 super Yang-Mills are dual to planar scattering amplitudes. This duality implies hidden symmetries for both objects. We consider closely related infrared finite observables, defined as the Wilson loop with a Lagrangian insertion, normalized by the Wilson loop itself. Unlike ratio and remainder functions studied in the literature, this observable is non-trivial already for four scattered particles and bears close resemblance to (finite parts of) scattering processes in non-supersymmetric Yang-Mills theory. Moreover, by integrating over the insertion point, one can recover information on the amplitude, as was recently done to compute the full four-loop cusp anomalous dimension. We study the general structure of the Wilson loop with a Lagrangian insertion, focusing in particular on its leading singularities and their (hidden) symmetry properties. Thanks to the close connection of the observable to integrands of MHV amplitudes, it is natural to expect that its leading singularities can be written as certain Grassmannian integrals. The latter are manifestly dual conformal. They also have a conformal symmetry, up to total derivatives. We find that, surprisingly, the conformal symmetry becomes an invariance in the frame where the Lagrangian insertion point is sent to infinity. Furthermore, we use integrability methods to study how higher Yangian charges act on the Grassmannian integral. We evaluate the n-particle observable both at tree- and at one-loop level, finding compact analytic formulas. These results are explicitly written in the form of conformal leading singularities, multiplied by transcendental functions. We then compare these formulas to known expressions for all-plus amplitudes in pure Yang-Mills theory. We find a remarkable new connection: the Wilson loop with Lagrangian insertion in $$ \mathcal{N} $$ N = 4 super Yang-Mills appears to predict the maximal weight terms of the planar pure Yang-Mills all-plus amplitude. We test this relationship for the two-loop n-point Yang-Mills amplitude, as well as for the three-loop four-point amplitude.

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Correlators with sℓ 2 Yangian symmetry

Cited by 7 publications

References 44 publications

Yangian symmetry for bi-scalar loop amplitudes

Yangian symmetry for bi-scalar loop amplitudes

Yangian and SUSY symmetry of high spin parton splitting amplitudes in generalised Yang–Mills theory

Symmetry properties of Wilson loops with a Lagrangian insertion

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