# 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}
}
• Published 29 February 2016
• Physics, Mathematics
• Journal of High Energy Physics
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…
15 Citations

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## References

SHOWING 1-10 OF 39 REFERENCES
On-shell diagrams, Graßmannians and integrability for form factors
• Physics, Mathematics
• 2015
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.
Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Physics, Mathematics
• 2014
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 identified
On-shell structures of MHV amplitudes beyond the planar limit
• Physics
• 2014
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 MHV
Non-planar on-shell diagrams
• Physics, Mathematics
• 2015
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 face
The geometry of on-shell diagrams
• Physics, Mathematics
• 2014
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 gauge
Yangians, Grassmannians and T-duality
• Physics
• 2010
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.
Logarithmic singularities and maximally supersymmetric amplitudes
• Physics
• 2014
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.
Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Physics
• 2009
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 the
Scattering Amplitudes and the Positive Grassmannian
• Physics, Mathematics
• 2012
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 physical
The all-loop integrand for scattering amplitudes in planar $\mathcal{N} = 4$ SYM
• Physics
• 2010
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. This