The connected prescription for form factors in twistor space

TL;DR

This paper introduces a new connected twistor space prescription for tree-level form factors in N=4 super Yang-Mills, linking it to scattering equations, BCFW recursion, and Grassmannian formulations, enhancing computational tractability.

Contribution

It generalizes the connected prescription to form factors, relates it to scattering equations, and connects it with BCFW recursion and Grassmannian approaches.

Findings

The formula matches recent scattering equations for form factors.

Link representation simplifies calculations compared to scattering equations.

The approach relates to Grassmannian and ambitwistor string formulations.

Abstract

We propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in $\mathcal{N}=4$ super Yang-Mills, which is a generalisation of the expression of Roiban, Spradlin and Volovich for superamplitudes. By introducing link variables, we show that our formula is identical to the recently proposed four-dimensional scattering equations for form factors. Similarly to the case of amplitudes, the link representation of form factors is shown to be directly related to BCFW recursion relations, and is considerably more tractable than the scattering equations. We also discuss how our results are related to a recent Grassmannian formulation of form factors, and comment on a possible derivation of our formula from ambitwistor strings.