Yangian Symmetry for Bi-Scalar Loop Amplitudes

Abstract

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. 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.

40 pages, 20 figures

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Cited by in corpus (44)

• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• Yangian Bootstrap for Conformal Feynman Integrals
• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Exact Correlation Functions in Conformal Fishnet Theory
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• All-loop singularities of scattering amplitudes in massless planar theories
• Massive Conformal Symmetry and Integrability for Feynman Integrals
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Continuum limit of fishnet graphs and AdS sigma model
• Hexagons and Correlators in the Fishnet Theory
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• The Double Box and Hexagon Conformal Feynman Integrals
• Yangian Bootstrap for Massive Feynman Integrals
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• Massive Fishnets
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Mirror channel eigenvectors of the $d$-dimensional fishnets
• The Loom for General Fishnet CFTs
• Exact scattering amplitudes in conformal fishnet theory
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$
• The Integrable (Hyper)eclectic Spin Chain
• Integrability for Feynman Integrals
• The Dual Conformal Box Integral in Minkowski Space
• Minkowski Box from Yangian Bootstrap
• ABJM quantum spectral curve and Mellin transform
• Hexagonalization of Fishnet integrals I: mirror excitations
• Yangian Symmetry in Holographic Correlators
• Yangian Algebra and Correlation Functions in Planar Gauge Theories
• Nonlocal Symmetries and Factorized Scattering
• Chaos in the Fishnet
• Twistor fishnets
• Checkerboard CFT
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Properties of the Conformal Yangian in Scalar and Gauge Field Theories
• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
• The Feyn-Structure of Yangian Symmetry
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Non-Local Symmetries of Planar Feynman Integrals
• A Large Twist Limit for Any Operator
• Separation of variables for higher rank integrable models: review of recent progress
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions