Ambitwistor Strings in Six and Five Dimensions

TL;DR

This paper develops twistor representations of ambitwistor strings in 6 and 5 dimensions, leading to models that describe various conformally invariant theories and supersymmetric gauge and gravity amplitudes.

Contribution

It introduces new twistor formulations of ambitwistor strings in higher dimensions and derives amplitude formulas for supersymmetric theories using polarized scattering equations.

Findings

Models describe biadjoint scalar, gauge, and gravity amplitudes.

Anomaly cancellation constrains models and relates to conformal invariance.

Derived explicit formulas for supersymmetric gauge and gravity amplitudes.

Abstract

Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4$^{\rm th}$ and 6$^{\rm th}$ order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formul{\ae} for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.