Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM

Abstract

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $\mathcal{N}=4$ SYM. For the off-shell amplitudes with one leg off-shell we present a conjecture for their Grassmannian integral representation in spinor helicity, twistor and momentum twistor parameterizations. The presented conjecture is successfully checked against BCFW results for MHV${}_n$, NMHV${}_4$ and NMHV${}_5$ off-shell amplitudes. We have also verified that our Grassmannian integral representation correctly reproduces soft (on-shell) limit for the off-shell gluon momentum. It is shown that the (deformed) off-shell amplitude expressions could be also obtained using quantum inverse scattering method for auxiliary $gl(4|4)$ super spin chain.

55 pages, 7 figures; v2: minor changes, typos corrected, references added

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Cited by in corpus (13)

• A Three-Point Form Factor Through Five Loops
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Full-color three-loop three-point form factors in N=4 SYM
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• The all-loop conjecture for integrands of reggeon amplitudes in N=4 SYM
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Form factors from string amplitudes
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• A connection between $\mathcal{R}$-invariants and Yang-Baxter $R$-operators in $\mathcal{N}=4$ super-Yang-Mills theory
• Wilson Lines and Boundary Operators of BCFW Shifts