On-shell Diagrams, Graßmannians and Integrability for Form Factors

Abstract

We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part of the stress-tensor multiplet as an example, we show how to systematically construct on-shell diagrams for these form factors with the minimal form factor as further building block in addition to the three-point amplitudes. Moreover, we obtain analytic representations in terms of Graßmannian integrals in spinor helicity, twistor and momentum twistor variables. While Yangian invariance is broken by the operator insertion, we find that the form factors are eigenstates of the integrable spin-chain transfer matrix built from the monodromy matrix that yields the Yangian generators. Constructing them via the method of R operators allows to introduce deformations that preserve the integrable structure. We finally show that the integrable properties extend to minimal tree-level form factors of generic composite operators as well as certain leading singularities of their n-point loop-level form factors.

44 pages, several figures; v2: References added, typos corrected, formulations clarified, 46 pages; v3: Conventions clarified, matches published version

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• Connected formulas for amplitudes in standard model
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• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Form Factor and Boundary Contribution of Amplitude
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• Yangian Symmetry for the Tree Amplituhedron
• Syzygies Probing Scattering Amplitudes
• The all-loop conjecture for integrands of reggeon amplitudes in N=4 SYM
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• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• A note on NMHV form factors from the Graßmannian and the twistor string
• Form factors from string amplitudes
• Boundary Perimeter Bethe Ansatz
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
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