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Amplitudes on plane waves from ambitwistor strings

Tim Adamo, Eduardo Casali, Lionel Mason, Stefan Nekovar

TL;DR

This work shows that ambitwistor strings can be consistently quantized on nontrivial curved backgrounds, specifically gravitational plane-wave spacetimes and plane-wave gauge fields, with anomaly cancellation tied to background equations of motion. It constructs explicit graviton and gluon vertex operators within the BRST framework and computes their 3-point sphere amplitudes, which reproduce the known field-theory results for these backgrounds. The results demonstrate that the ambitwistor approach yields a practical, purely stringy method to study perturbative QFT on curved spaces, offering a platform for higher-point extensions and exploration of other backgrounds and the gravity–gauge theory double-copy relation in nontrivial geometries. This establishes a bridge between free worldsheet CFT techniques and curved-space scattering, with potential implications for holography and beyond.

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.

Amplitudes on plane waves from ambitwistor strings

TL;DR

This work shows that ambitwistor strings can be consistently quantized on nontrivial curved backgrounds, specifically gravitational plane-wave spacetimes and plane-wave gauge fields, with anomaly cancellation tied to background equations of motion. It constructs explicit graviton and gluon vertex operators within the BRST framework and computes their 3-point sphere amplitudes, which reproduce the known field-theory results for these backgrounds. The results demonstrate that the ambitwistor approach yields a practical, purely stringy method to study perturbative QFT on curved spaces, offering a platform for higher-point extensions and exploration of other backgrounds and the gravity–gauge theory double-copy relation in nontrivial geometries. This establishes a bridge between free worldsheet CFT techniques and curved-space scattering, with potential implications for holography and beyond.

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.

Paper Structure

This paper contains 14 sections, 95 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Worldsheet Models
  3. Ambitwistor strings in flat space
  4. Type II model on a curved background metric
  5. Heterotic model on a gauge field background
  6. Type II Model on a Gravitational Plane Wave
  7. Plane wave metrics & Scattering
  8. Worldsheet model and Vertex operators
  9. 3-point function
  10. Heterotic Model on a Gauge Field Plane Wave Background
  11. Plane wave gauge fields & Scattering
  12. Worldsheet model and Vertex operators
  13. 3-point function
  14. Discussion

Figures (1)

  • Figure 1: A two dimensional Penrose diagram of a sandwich plane wave, ignoring the spatial directions. While the far past and future are flat, the grey region defined by $u_1\le u \le u_2$ has non-vanishing curvature.