Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM

TL;DR

This paper introduces a Grassmannian integral representation for gauge invariant off-shell amplitudes in N=4 SYM, including purely off-shell cases, verified through examples and linked to quantum inverse scattering methods.

Contribution

It proposes a novel Grassmannian integral formula for off-shell amplitudes in N=4 SYM, extending the framework to purely off-shell scenarios and connecting with super spin chain techniques.

Findings

Grassmannian integral representation verified for several examples

Formulation applicable to purely off-shell objects without on-shell particles

Off-shell amplitudes derived using quantum inverse scattering method

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.