Connecting the ambitwistor and the sectorized heterotic strings

TL;DR

This paper clarifies the relationship between ambitwistor and sectorized heterotic strings, revealing their spectrum, higher curvature contributions, and the connection through a parameter limit, thus resolving misconceptions about their tension.

Contribution

It demonstrates that the sectorized heterotic string model is two-fold depending on the supersymmetric sector and connects it to the ambitwistor string via a specific limit.

Findings

The heterotic string spectrum includes a massive multiplet and higher curvature terms.

Reintroducing a parameter $\, ext{ extltilde}\, ext{ extltilde}$ reveals the two-fold nature of the model.

The ambitwistor string is obtained as a limit of the sectorized heterotic string.

Abstract

The sectorized description of the (chiral) heterotic string using pure spinors has been misleadingly viewed as an infinite tension string. One evidence for this fact comes from the tree level 3-point graviton amplitude, which we show to contain the usual Einstein term plus a higher curvature contribution. After reintroducing a dimensionful parameter $\ell$ in the theory, we demonstrate that the heterotic model is in fact two-fold, depending on the choice of the supersymmetric sector, and that the spectrum also contains one massive (open string like) multiplet. By taking the $\ell\to\infty$ limit, we finally show that the ambitwistor string is recovered, reproducing the unexpected heterotic state in Mason and Skinner's RNS description.