A note on NMHV form factors from the Gra{\ss}mannian and the twistor string

摘要

In this note we investigate Gra{\ss}mannian formulas for form factors of thechiral part of the stress-tensor multiplet in $\mathcal{N}=4$ superconformalYang-Mills theory. We present an all-$n$ contour for the $G(3,n+2)$Gra{\ss}mannian integral of NMHV form factors derived from on-shell diagramsand the BCFW recursion relation. In addition, we study other $G(3,n+2)$formulas obtained from the connected prescription introduced recently. We finda recursive expression for all $n$ and study its properties. For $n \geq 6$,our formula has the same recursive structure as its amplitude counterpart,making its soft behaviour manifest. Finally, we explore the connection betweenthe two Gra{\ss}mannian formulations, using the global residue theorem, andfind that it is much more intricate compared to scattering amplitudes.