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Connecting the ambitwistor and the sectorized heterotic strings

Thales Azevedo, Renann Lipinski Jusinskas

TL;DR

The paper clarifies the fate of the sectorized heterotic string by introducing a dimensionful length scale $ ext{ extellipsis}$ and formulating two inequivalent sectors (A and B). At finite $ ext{ extellipsis}$, the B model hosts a massive open-string–like multiplet with $M^{2}=4/ ext{ extellipsis}^{2}$, while the A model remains massless; in the $ ext{ extellipsis} o ext{ extellipsis}$ limit, the theory becomes the heterotic ambitwistor string with BRST charge $Q= ext{``} ext{ extellipsis}+ rac{1}{4}ar{c}P^{m}P_{m} ext{''}$, recovering Mason–Skinner’s gravity sector and revealing an extra 3-form and related states. The work demonstrates that the ambitwistor string emerges as the tensionless limit of the sectorized model, with a Galilean conformal structure and a nuanced cohomology that includes both massless supergravity and additional massless/massive states, thereby connecting twisted and chiral string theories. It also highlights a potential missing vector degree of freedom relative to Mason–Skinner's spectrum and discusses covariant, light-cone, and DDF-type constructions for the massive sector, laying groundwork for further study of integrated vertices and background couplings in these chiral theories.

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.

Connecting the ambitwistor and the sectorized heterotic strings

TL;DR

The paper clarifies the fate of the sectorized heterotic string by introducing a dimensionful length scale and formulating two inequivalent sectors (A and B). At finite , the B model hosts a massive open-string–like multiplet with , while the A model remains massless; in the limit, the theory becomes the heterotic ambitwistor string with BRST charge , recovering Mason–Skinner’s gravity sector and revealing an extra 3-form and related states. The work demonstrates that the ambitwistor string emerges as the tensionless limit of the sectorized model, with a Galilean conformal structure and a nuanced cohomology that includes both massless supergravity and additional massless/massive states, thereby connecting twisted and chiral string theories. It also highlights a potential missing vector degree of freedom relative to Mason–Skinner's spectrum and discusses covariant, light-cone, and DDF-type constructions for the massive sector, laying groundwork for further study of integrated vertices and background couplings in these chiral theories.

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 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 limit, we finally show that the ambitwistor string is recovered, reproducing the unexpected heterotic state in Mason and Skinner's RNS description.

Paper Structure

This paper contains 12 sections, 82 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The sectorized model and the dimensionful parameter
  3. 3-point tree-level amplitude for gravitons
  4. Dimensionful parameter
  5. Alternative formulation
  6. Cohomology
  7. Light-cone description of the massive states
  8. The $\ell\to\infty$ limit and the connection to ambitwistor strings
  9. The heterotic ambitwistor string in the pure spinor formalism
  10. The light-cone analysis of the ambitwistor cohomology
  11. Concluding remarks
  12. Useful OPE's

Figures (1)

  • Figure 1: On the left we have the $SO(8)$ degrees of freedom of the massive vertex \ref{['eq:LC-massive-open']}. On the right side, after taking the limit $\ell \to \infty$, we are left with two partially independent massless multiplets, connected only by the algebra \ref{['eq:wrongSUSY-massless']}.