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 , NMHV4 and NMHV5 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 \( \mathfrak{g}\mathfrak{l}\left(4\Big|4\right) \) super spin chain.
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Bork, L.V., Onishchenko, A.I. Wilson lines, Grassmannians and gauge invariant off-shell amplitudes in \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2017, 19 (2017). https://doi.org/10.1007/JHEP04(2017)019
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DOI: https://doi.org/10.1007/JHEP04(2017)019