The SAGEX Review on Scattering Amplitudes, Chapter 6: Ambitwistor Strings and Amplitudes from the Worldsheet

TL;DR

This chapter reviews ambitwistor string theories that produce compact, worldsheet-based formulas for scattering amplitudes in various field theories, highlighting their structure, applications, and connections to broader string theory concepts.

Contribution

It introduces two formulations of ambitwistor strings, demonstrating their ability to derive scattering amplitudes and explore new theoretical and practical applications.

Findings

Derivation of compact formulas for tree-level amplitudes and loop integrands.

Manifestation of double copy relations at the worldsheet level.

Applications to curved backgrounds and extensions to new sectors.

Abstract

Starting with Witten's twistor string, chiral string theories have emerged that describe field theory amplitudes without the towers of massive states of conventional strings. These models are known as ambitwistor strings due to their target space; the space of complexified null geodesics, also called ambitwistor space. Correlators in these string theories directly yield compact formulae for tree-level amplitudes and loop integrands, in the form of worldsheet integrals fully localized on solutions to constraints known as the scattering equations. In this chapter, we discuss two incarnations of the ambitwistor string: a 'vector representation' starting in space-time and structurally resembling the RNS superstring, and a four-dimensional twistorial version closely related to, but distinct from Witten's original model. The RNS-like models exist for several theories, with 'heterotic' and type II models describing super-Yang-Mills and 10d supergravities respectively, and they manifest the double copy relations directly at the level of the worldsheet models. In the second half of the chapter, we explain how the underlying models lead to diverse applications, ranging from extensions to new sectors of theories, loop amplitudes and to scattering on curved backgrounds. We conclude with a brief discussion of connections to conventional strings and celestial holography.