Ambitwistor string vertex operators on curved backgrounds

TL;DR

This work demonstrates that ambitwistor strings defined on curved backgrounds yield exact, BRST-cohomology-based conditions that reproduce linearized field equations for perturbations without performing a background-field expansion. It constructs explicit vertex operators in the fixed (-1,-1) picture for the heterotic model (gluon) and the Type II model (graviton, B-field, dilaton), revealing how BRST closure imposes gauge-fixing and linearized equations on perturbations. For the Type II theory, a unified NS-NS vertex operator (the fat graviton) resolves issues arising from treating the three NS-NS sectors separately, enforcing the full linearized NS-NS supergravity equations under a generalized de Donder gauge. The results illustrate the exactness and potential of ambitwistor strings in curved backgrounds while also outlining technical challenges in descent, integration, and the GSO projection, pointing toward future work on higher-point amplitudes and more complete curved-space formulations.

Abstract

We present vertex operators for ambitwistor strings around generic Yang-Mills, gravity and NS-NS backgrounds. The requirement that vertex operators lie in the BRST cohomology of the worldsheet theory enforces the appropriate linear equations of motion (as well as gauge fixing conditions) for the respective perturbations in these backgrounds. Due to the nature of ambitwistor strings, no approximation is taken and all calculations around the backgrounds are exact.