Yangian-type symmetries of non-planar leading singularities

@article{Frassek2016YangiantypeSO,
  title={Yangian-type symmetries of non-planar leading singularities},
  author={Rouven Frassek and David Meidinger},
  journal={Journal of High Energy Physics},
  year={2016},
  volume={2016},
  pages={1-12}
}
A bstractWe take up the study of integrable structures behind non-planar contributions to scattering amplitudes in N=4$$ \mathcal{N}=4 $$ super Yang-Mills theory. Focusing on leading singularities, we derive the action of the Yangian generators on color-ordered subsets of the external states. Each subset corresponds to a single boundary of the non-planar on-shell diagram. While Yangian invariance is broken, we find that higher-level Yangian generators still annihilate the non-planar on-shell… Expand

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References

SHOWING 1-10 OF 39 REFERENCES
On-shell diagrams, Graßmannians and integrability for form factors
A bstractWe apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4$$ \mathcal{N}=4 $$ SYM theory to tree-level form factors of this theory.Expand
Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
We propose that Baxter’s Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identifiedExpand
On-shell structures of MHV amplitudes beyond the planar limit
A bstractWe initiate an exploration of on-shell functions in N=4$$ \mathcal{N}=4 $$ SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHVExpand
Non-planar on-shell diagrams
A bstractWe initiate a systematic study of non-planar on-shell diagrams in N=4$$ \mathcal{N}=4 $$ SYM and develop powerful technology for doing so. We introduce canonical variables generalizing faceExpand
The geometry of on-shell diagrams
A bstractThe fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gaugeExpand
Yangians, Grassmannians and T-duality
We investigate the Yangian symmetry of scattering amplitudes in $$ \mathcal{N} = 4 $$ super Yang-Mills theory and show that its formulations in twistor and momentum twistor space can be interchanged.Expand
Logarithmic singularities and maximally supersymmetric amplitudes
A bstractThe dual formulation of planar N=4$$ \mathcal{N}=4 $$ super-Yang-Mills scattering amplitudes makes manifest that the integrand has only logarithmic singularities and no poles at infinity.Expand
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Tree-level scattering amplitudes in = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending theExpand
Scattering Amplitudes and the Positive Grassmannian
We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physicalExpand
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
We give an explicit recursive formula for the all ℓ-loop integrand for scattering amplitudes in $ \mathcal{N} = 4 $ SYM in the planar limit, manifesting the full Yangian symmetry of the theory. ThisExpand
...
1
2
3
4
...