A Superstring Field Theory for Supergravity

TL;DR

This work develops a covariant, BRST-based string field theory for the ambitwistor string, whose massless spectrum and amplitudes reproduce ten-dimensional Type II supergravity. It constructs both bosonic and supersymmetric ambitwistor string fields, derives a quadratic action that yields the linearised Fierz-Pauli and NS-NS Type II actions, and proposes a non-polynomial interaction structure built from an infinite set of vertices tied to moduli-space regions. The formalism links on-shell amplitudes to surface-state calculations and CHY scattering equations, and it discusses picture-changing, off-shell extensions, as well as potential curved-background generalisations and Ramond-sector completion. While challenges remain—most notably a complete geometric understanding of the propagator and proving the main identity in the supersymmetric case—the framework offers a tractable, covariant toy model for gravity within a string-field-like setting and suggests connections to localisation in moduli space.

Abstract

A covariant closed superstring field theory, equivalent to classical ten-dimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the Neveu-Schwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.