Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory

TL;DR

This paper extends the twistor-space formulation of $ abla=4$ Super Yang-Mills theory to include gauge-invariant local composite operators, enabling the computation of form factors within this framework.

Contribution

It introduces a method to incorporate composite operators into twistor space and demonstrates this by calculating form factors for scalar operators.

Findings

Successful definition of composite operators in twistor space

Calculation of form factors for scalar operators

Establishment of a framework for studying form factors in twistor space

Abstract

We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper.