Built on

A. B. Zamolodchikov, ‘Fishnet’ Diagrams as a Completely Integrable System
1980
Earlier work this paper cites.
V. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation
1985
Earlier work this paper cites.
N. Ussyukina and A. I. Davydychev, An approach to the evaluation of three-and four-point ladder diagrams
1993
Earlier work this paper cites.
hep-th/9605187
L. D. Faddeev, How algebraic Bethe ansatz works for integrable model · 1996
Earlier work this paper cites.
A. Molev, M. Nazarov, and G. Olshansky, Yangians and classical Lie algebras
1996
Earlier work this paper cites.
J. M. Maldacena, Wilson loops in large N field theories
1998
Earlier work this paper cites.
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity
2001
Earlier work this paper cites.
S. E. Derkachov and A. N. Manashov, R-matrix and baxter Q-operators for the noncompact SL(N,C) invariant spin chain
2006
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling
Original
2007
Earlier work this paper cites.
J. M. Drummond, G. P. Korchemsky, and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops
Original
2008
Earlier work this paper cites.
J. M. Drummond, J. M. Henn, and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Original
2009
Earlier work this paper cites.
S. E. Derkachov and A. N. Manashov, General solution of the Yang-Baxter equation with symmetry group SL(n,C)
2009
Earlier work this paper cites.
J. M. Drummond, J. M. Henn, and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Original
2009
Earlier work this paper cites.
J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
Original
2010
Earlier work this paper cites.

Similar

N. Beisert, J. Henn, T. McLoughlin, and J. Plefka, One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
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2010
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J. M. Henn, Dual conformal symmetry at loop level: massive regularization
Original
2011
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2012
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Original

Then

R. Frassek, N. Kanning, Y. Ko, and M. Staudacher, Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
Original
2014
Later among the works it cites.
N. Kanning, T. Lukowski, and M. Staudacher, A shortcut to general tree-level scattering amplitudes in 𝒩 = 4 \mathcal{N}=4 SYM via integrability
Original
2014
Later among the works it cites.
J. Broedel, M. de Leeuw, and M. Rosso, A dictionary between R-operators, on-shell graphs and Yangian algebras
Original
2014
Later among the works it cites.
R. Kirschner, Yangian symmetric correlators, R operators and amplitudes
2014
Later among the works it cites.
N. Gromov, V. Kazakov, S. Leurent, and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5 /CFT 4
2015

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2017

Yangian Symmetry for Bi-Scalar Loop Amplitudes

Chicherin, Dmitry, Kazakov, Vladimir, Loebbert, Florian et al.

Understand

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 gamma-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.

Built on

A. B. Zamolodchikov, ‘Fishnet’ Diagrams as a Completely Integrable System
1980
Earlier work this paper cites.
V. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation
1985
Earlier work this paper cites.
N. Ussyukina and A. I. Davydychev, An approach to the evaluation of three-and four-point ladder diagrams
1993
Earlier work this paper cites.
hep-th/9605187
L. D. Faddeev, How algebraic Bethe ansatz works for integrable model · 1996
Earlier work this paper cites.
A. Molev, M. Nazarov, and G. Olshansky, Yangians and classical Lie algebras
1996
Earlier work this paper cites.
J. M. Maldacena, Wilson loops in large N field theories
1998
Earlier work this paper cites.
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity
2001
Earlier work this paper cites.
S. E. Derkachov and A. N. Manashov, R-matrix and baxter Q-operators for the noncompact SL(N,C) invariant spin chain
2006
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling
Original
2007
Earlier work this paper cites.
J. M. Drummond, G. P. Korchemsky, and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops
Original
2008
Earlier work this paper cites.
J. M. Drummond, J. M. Henn, and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Original
2009
Earlier work this paper cites.
S. E. Derkachov and A. N. Manashov, General solution of the Yang-Baxter equation with symmetry group SL(n,C)
2009
Earlier work this paper cites.
J. M. Drummond, J. M. Henn, and J. Plefka, Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
Original
2009
Earlier work this paper cites.
J. M. Drummond, J. Henn, G. P. Korchemsky, and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
Original
2010
Earlier work this paper cites.

Similar

N. Beisert, J. Henn, T. McLoughlin, and J. Plefka, One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
Original
2010
Cited alongside, same era.
R. Roiban, M. Spradlin, and A. Volovich, Scattering amplitudes in gauge theories: progress and outlook Scattering amplitudes in gauge theories: progress and outlook
2011
Cited alongside, same era.
J. M. Henn, Dual conformal symmetry at loop level: massive regularization
Original
2011
Cited alongside, same era.
N. Beisert et al., Review of AdS/CFT Integrability: An Overview
Original
2012
Cited alongside, same era.
S. Caron-Huot and S. He, Jumpstarting the All-Loop S-Matrix of Planar N=4 Super Yang-Mills
Original

Then

R. Frassek, N. Kanning, Y. Ko, and M. Staudacher, Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
Original
2014
Later among the works it cites.
N. Kanning, T. Lukowski, and M. Staudacher, A shortcut to general tree-level scattering amplitudes in 𝒩 = 4 \mathcal{N}=4 SYM via integrability
Original
2014
Later among the works it cites.
J. Broedel, M. de Leeuw, and M. Rosso, A dictionary between R-operators, on-shell graphs and Yangian algebras
Original
2014
Later among the works it cites.
R. Kirschner, Yangian symmetric correlators, R operators and amplitudes
2014
Later among the works it cites.
N. Gromov, V. Kazakov, S. Leurent, and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS 5 /CFT 4
2015

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2012

Cited alongside, same era.

Cambridge University Press, 2012

N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov, and J. Trnka, Scattering Amplitudes and the Positive Grassmannian · 2012

Cited alongside, same era.

B. Basso, A. Sever, and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N=4 Supersymmetric Yang-Mills Theory

Original

2013

Cited alongside, same era.

D. Chicherin and R. Kirschner, Yangian symmetric correlators

Original

2013

Cited alongside, same era.

D. Chicherin, S. Derkachov, and A. P. Isaev, Conformal group: R-matrix and star-triangle relation

Original

2013

Cited alongside, same era.

J. Drummond, C. Duhr, B. Eden, P. Heslop, J. Pennington, and V. A. Smirnov, Leading singularities and off-shell conformal integrals

Original

2013

Cited alongside, same era.

N. Gromov, V. Kazakov, S. Leurent, and D. Volin, Quantum Spectral Curve for Planar 𝒩 = \mathcal{N}= Super-Yang-Mills Theory

2014

Cited alongside, same era.

J. Fokken, C. Sieg, and M. Wilhelm, A piece of cake: the ground-state energies in γ i \gamma_{i} -deformed 𝒩 \mathcal{N} = 4 SYM theory at leading wrapping order

2014

Cited alongside, same era.

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T. Bargheer, Y.-t. Huang, F. Loebbert, and M. Yamazaki, Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory

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2015

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L. V. Bork and A. I. Onishchenko, On soft theorems and form factors in 𝒩 = 4 \mathcal{N}=4 SYM theory

Original

2015

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T. Fleury and S. Komatsu, Hexagonalization of correlation functions