Grassmannians and form factors with $q^2=0$ in N=4 SYM theory

TL;DR

This paper proposes a Grassmannian integral representation for tree-level form factors with light-like momentum in N=4 SYM, verified through known cases and soft limit analysis.

Contribution

It introduces a conjecture for Grassmannian formulas for form factors with $q^2=0$ in N=4 SYM, extending the geometric approach to these objects.

Findings

Successfully reproduces known MHV and N$^{k-2}$MHV form factors

Demonstrates cancellation of spurious poles

Explores relations between different BCFW representations

Abstract

We consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum $q^2=0$. We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts. The presented conjecture was successfully checked by reproducing several known answers in $\mbox{MHV}$ and $\mbox{N}^{k-2}\mbox{MHV}$, $k\geq3$ sectors together with appropriate soft limits. We also discuss the cancellation of spurious poles and relations between different BCFW representations for such form factors on simple examples.