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New Ambitwistor String Theories

Eduardo Casali, Yvonne Geyer, Lionel Mason, Ricardo Monteiro, Kai A. Roehrig

TL;DR

The paper surveys a family of new ambitwistor string theories that reproduce the Cachazo–He–Yuan amplitude formulae for Einstein–Yang–Mills, Dirac–Born–Infeld, Galileons and related theories by introducing novel worldsheet CFTs (notably the comb system) to generate correct color factors without spurious multitrace terms. It analyzes how different left/right matter combinations yield CHY-like building blocks—Pfaffians, determinants, and Parke–Taylor factors—for a range of space-time theories, including an anomaly-free Einstein–Yang–Mills model via a comb-based construction and a linearized $T^*\mathrm{YM}$ description with doubled gluons. The work discusses central charges, critical dimensions, and BRST consistency across models, and presents detailed correlator constructions (e.g., $\mathrm{Pf}'\, M$, $\mathrm{Pf}'\, \Pi$, and comb structures $\mathcal{C}$) that realize the CHY integrands at tree level, with extensions to YM, bi-adjoint scalars, and beyond. It highlights key challenges for loops (modularity, anomalies) and outlines directions for incorporating Ramond sectors and loop amplitudes within this ambitwistor framework, including potential modular invariant completions. Overall, the paper establishes a unifying string-theoretic origin for a broad class of CHY amplitudes and clarifies the roles of new worldsheet matter systems in achieving consistent, theory-specific color-kinematics structures.

Abstract

We describe new ambitwistor string theories that give rise to the recent amplitude formulae for Einstein-Yang-Mills, (Dirac)-Born-Infeld, Galileons and others introduced by Cachazo, He and Yuan. In the case of the Einstein-Yang-Mills amplitudes, an important role is played by a novel worldsheet conformal field theory that provides the appropriate colour factors precisely without the spurious multitrace terms of earlier models that had to be ignored by hand. This is needed to obtain the correct multitrace terms that arise when Yang-Mills is coupled to gravity.

New Ambitwistor String Theories

TL;DR

The paper surveys a family of new ambitwistor string theories that reproduce the Cachazo–He–Yuan amplitude formulae for Einstein–Yang–Mills, Dirac–Born–Infeld, Galileons and related theories by introducing novel worldsheet CFTs (notably the comb system) to generate correct color factors without spurious multitrace terms. It analyzes how different left/right matter combinations yield CHY-like building blocks—Pfaffians, determinants, and Parke–Taylor factors—for a range of space-time theories, including an anomaly-free Einstein–Yang–Mills model via a comb-based construction and a linearized description with doubled gluons. The work discusses central charges, critical dimensions, and BRST consistency across models, and presents detailed correlator constructions (e.g., , , and comb structures ) that realize the CHY integrands at tree level, with extensions to YM, bi-adjoint scalars, and beyond. It highlights key challenges for loops (modularity, anomalies) and outlines directions for incorporating Ramond sectors and loop amplitudes within this ambitwistor framework, including potential modular invariant completions. Overall, the paper establishes a unifying string-theoretic origin for a broad class of CHY amplitudes and clarifies the roles of new worldsheet matter systems in achieving consistent, theory-specific color-kinematics structures.

Abstract

We describe new ambitwistor string theories that give rise to the recent amplitude formulae for Einstein-Yang-Mills, (Dirac)-Born-Infeld, Galileons and others introduced by Cachazo, He and Yuan. In the case of the Einstein-Yang-Mills amplitudes, an important role is played by a novel worldsheet conformal field theory that provides the appropriate colour factors precisely without the spurious multitrace terms of earlier models that had to be ignored by hand. This is needed to obtain the correct multitrace terms that arise when Yang-Mills is coupled to gravity.

Paper Structure

This paper contains 25 sections, 3 theorems, 87 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Ambitwistor string models
  3. The bosonic ambitwistor string
  4. Vertex operators and worldsheet matter
  5. Worldsheet matter models and their correlators
  6. Free fermions S-rho and current algebras S-j.
  7. Worldsheet suspersymmetry S-Psi.
  8. Comb system S-CS.
  9. Other systems with comb structure, S-YM.
  10. Central charges
  11. Combined Matter models
  12. S-rho,Psi
  13. S-Psi1,Psi2
  14. S-YM,Psi
  15. S-CS,Psi
  16. ...and 10 more sections

Key Result

Proposition 3.1

Correlators of the currents $u,v,\tilde{u},\tilde{v}$ are only nonvanishing when there is just one untilded current and give where

Figures (2)

  • Figure 1: Theories studied by CHY and operations relating them.
  • Figure 2: Charge flows

Theorems & Definitions (3)

  • Proposition 3.1: Casali-Skinner
  • Theorem 1
  • Theorem 2