Grassmannian Integral for General 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 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 $\mathfrak{gl}(4|4)$ super spin chain.

38 pages, 9 figures; v4: typos corrected, comment in section 3.2 added

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Cited by in corpus (6)

• 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
• Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Boundary Perimeter Bethe Ansatz
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space