Wilson lines, Grassmannians and 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, verified through BCFW results and soft limit checks, connecting to integrable systems.

Contribution

It proposes a novel Grassmannian integral formula for off-shell amplitudes in N=4 SYM, validated against known results and linked to quantum inverse scattering methods.

Findings

Grassmannian integral representation matches BCFW calculations

Correctly reproduces soft limit behavior

Connects off-shell amplitudes to integrable spin chain models

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 MHV$_n$, NMHV$_4$ and NMHV$_5$ 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 $gl(4|4)$ super spin chain.