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 MHVn, 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(4Big|4right) super spin chain.
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