Lectures on twistor theory

TL;DR

This paper provides an overview of twistor theory, highlighting its geometric encoding of space-time, its historical successes and challenges, and recent advances in applying it to perturbative quantum field theory.

Contribution

It offers a comprehensive review of twistor theory's development, its key applications, and recent progress in addressing past limitations, especially in quantum field theory contexts.

Findings

Successful description of free fields using twistor methods

Recent advances overcoming historical limitations

Application of twistor theory to perturbative QFT

Abstract

Broadly speaking, twistor theory is a framework for encoding physical information on space-time as geometric data on a complex projective space, known as a twistor space. The relationship between space-time and twistor space is non-local and has some surprising consequences, which we explore in these lectures. Starting with a review of the twistor correspondence for four-dimensional Minkowski space, we describe some of twistor theory's historic successes (e.g., describing free fields and integrable systems) as well as some of its historic shortcomings. We then discuss how in recent years many of these problems have been overcome, with a view to understanding how twistor theory is applied to the study of perturbative QFT today. These lectures were given in 2017 at the XIII Modave Summer School in mathematical physics.