A note on connected formula for form factors

TL;DR

This paper explores a connected prescription derived from twistor string theory for calculating tree-level form factors in ${ m N}=4$ super-Yang-Mills theory, proposing universal formulas for various operators.

Contribution

It introduces a universal connected formula for form factors using four-dimensional scattering equations applicable to general operators.

Findings

Proposes compact formulas for super form factors with chiral stress-tensor multiplet.

Provides formulas for bosonic form factors with scalar operators ${\rm Tr}(\phi^m)$.

Demonstrates the universality of the connected prescription.

Abstract

In this note we study the connected prescription, originally derived from Witten's twistor string theory, for tree-level form factors in ${\cal N}=4$ super-Yang-Mills theory. The construction is based on the recently proposed four-dimensional scattering equations with $n$ massless on-shell states and one off-shell state, which we expect to work for form factors of general operators. To illustrate the universality of the prescription, we propose compact formulas for super form factors with chiral stress-tensor multiplet operator, and bosonic ones with scalar operators ${\rm Tr}(\phi^m)$ for arbitrary $m$.