Abstract
In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in \( \mathcal{N}=4 \) SYM with arbitrary number of off-shell gluons or equivalently Wilson line operator insertions. We make a conjecture for the Grassmannian integral representation for such objects and verify our conjecture on several examples. It is remarkable that in our formulation one can consider situation when on-shell particles are not present at all, i.e. we have Grassmannian integral representation for purely off-shell object. In addition we show that off-shell amplitude with arbitrary number of off-shell gluons 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., Onishchenko, A. Grassmannian integral for general gauge invariant off-shell amplitudes in \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2017, 40 (2017). https://doi.org/10.1007/JHEP05(2017)040
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DOI: https://doi.org/10.1007/JHEP05(2017)040