Loops in Twistor Space

TL;DR

This paper explores the structure of one-loop MHV diagrams in twistor space, addressing infrared divergences, introducing a twistor-space regulator, and analyzing the holomorphic anomaly to understand amplitude structures.

Contribution

It provides a detailed analysis of one-loop twistor-space structures, introduces a twistor-space regulator for infrared divergences, and examines the holomorphic anomaly to probe amplitude geometry.

Findings

Infrared divergences are limited to specific MHV diagrams.

A twistor-space regulator analogous to dimensional regularization is proposed.

Explicit evaluation of the holomorphic anomaly informs the structure of one-loop amplitudes.

Abstract

We elucidate the one-loop twistor-space structure corresponding to momentum-space MHV diagrams. We also discuss the infrared divergences, and argue that only a limited set of MHV diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the `holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.