Amplitudes on plane waves from ambitwistor strings

TL;DR

This paper demonstrates that ambitwistor strings can be quantized on plane wave backgrounds, deriving vertex operators and reproducing known 3-point scattering amplitudes for gravitons and gluons in these backgrounds.

Contribution

It provides a novel analysis of ambitwistor strings on curved backgrounds, specifically plane waves, and derives explicit vertex operators and correlation functions.

Findings

Worldsheet models are anomaly free on plane wave backgrounds.

Vertex operators for gravitons and gluons are constructed explicitly.

3-point functions match known scattering amplitudes in these backgrounds.

Abstract

In marked contrast to conventional string theory, ambitwistor strings remain solvable worldsheet theories when coupled to curved background fields. We use this fact to consider the quantization of ambitwistor strings on plane wave metric and plane wave gauge field backgrounds. In each case, the worldsheet model is anomaly free as a consequence of the background satisfying the field equations. We derive vertex operators (in both fixed and descended picture numbers) for gravitons and gluons on these backgrounds from the worldsheet CFT, and study the 3-point functions of these vertex operators on the Riemann sphere. These worldsheet correlation functions reproduce the known results for 3-point scattering amplitudes of gravitons and gluons in gravitational and gauge theoretic plane wave backgrounds, respectively.