Field theory actions for ambitwistor string and superstring

TL;DR

This work analyzes free ambitwistor string field theories across bosonic, heterotic, and Type II sectors, showing that only the $GSO(+)$ Type II sector yields the conventional $d=10$ $N=2$ supergravity spectrum, while the other sectors harbor non-unitary massless states. Using BRST cohomology at ghost-number $2$ and a standard closed-string field theory framework, the authors derive quadratic kinetic terms for the ambitwistor string fields, uncovering higher-derivative dynamics (e.g., terms like $R_{mn}oxempty R^{mn}$ and $oxempty^3$-type operators) that reconcile with the momentum structure of the scattering amplitudes. They provide explicit kinetic actions for the bosonic, Type II, and heterotic ambitwistor strings, including gauge-invariant reformulations and, in the Type II and heterotic cases, reveal nontrivial spectra such as extra antisymmetric forms or 3-forms. The results offer a platform to test one-loop ambitwistor prescriptions against non-unitary sectors and suggest routes to extending the quadratic theory to interacting actions, with potential connections to higher-derivative or conformal gravity regimes. Overall, the paper clarifies the spectrum and kinetic structure of ambitwistor string field theories and their implications for both tree and loop-level consistency checks.

Abstract

We analyze the free ambitwistor string field theory action for the bosonic string, heterotic string and both GSO sectors of the Type II string. The spectrum contains non-unitary states and provides an interesting consistency test for one-loop ambitwistor string computations.