On Form Factors and Correlation Functions in Twistor Space

TL;DR

This paper advances the twistor-space approach to N=4 super Yang-Mills theory by developing methods to compute form factors and correlation functions, including loop-level extensions, using position and momentum twistors.

Contribution

It introduces a systematic way to calculate twistor-space diagrams for general form factors and relates position-twistor and momentum-twistor formalisms, extending to loop levels.

Findings

Derived twistor-space diagrams for N^kMHV form factors.

Reexpressed NMHV form factors in momentum twistor variables.

Extended the formalism to include loop-level calculations.

Abstract

In this paper, we continue our study of form factors and correlation functions of gauge-invariant local composite operators in the twistor-space formulation of N=4 super Yang-Mills theory. Using the vertices for these operators obtained in our recent papers arXiv:1603.04471 and arXiv:1604.00012, we show how to calculate the twistor-space diagrams for general N^kMHV form factors via the inverse soft limit, in analogy to the amplitude case. For general operators without $\dot\alpha$ indices, we then reexpress the NMHV form factors from the position-twistor calculation in terms of momentum twistors, deriving and expanding on a relation between the two twistor formalisms previously observed in the case of amplitudes. Furthermore, we discuss the calculation of generalized form factors and correlation functions as well as the extension to loop level, in particular providing an argument promised in arXiv:1410.6310.