Grassmannian integral for general gauge invariant off-shell amplitudes in N = 4 $$ \mathcal{N}=4 $$ SYM

Abstract

Abstract In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in N = 4 $$ \mathcal{N}=4 $$ 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 g l 4 | 4 $$ \mathfrak{g}\mathfrak{l}\left(4\Big|4\right) $$ super spin chain.

Keywords

• Scattering Amplitudes
• Supersymmetric Gauge Theory
• Integrable Field Theories
• Extended Supersymmetry