Ambitwistor strings and the scattering equations
Lionel Mason, David Skinner
TL;DR
Ambitwistor strings provide a chiral, tensionless limit of string theory whose massless spectrum reproduces the Cachazo-He-Yuan tree-level scattering amplitudes in arbitrary dimensions. By formulating worldsheet theories on ambitwistor space and its supersymmetric extension, the authors derive vertex operators whose correlators localize on the scattering equations $\sum_{j\neq i} \frac{k_i\cdot k_j}{σ_i-σ_j}=0$ with $P(σ)=\sum_i \frac{k_i}{σ-σ_i}$, yielding gravity, Yang-Mills, and scalar amplitudes via Pfaffians and current algebra correlators. The framework unifies twistor and ambitwistor ideas, offers a geometric basis for the scattering equations beyond four dimensions, and points to natural extensions to loop level and Ramond sectors, potentially providing a route to a field-theory action with BCJ duality underlying these amplitudes.
Abstract
We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space--time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree--level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories.