Massive ambitwistor-strings; twistorial models

TL;DR

This paper extends ambitwistor-string models to include massive particles in 4d, providing new systematic rules and formulae for calculating scattering amplitudes in massive gauge and gravity theories with a double copy structure.

Contribution

It introduces a systematic reduction from higher dimensions to 4d for massive ambitwistor models, resulting in new formulae for amplitudes in massive gauge and supergravity theories.

Findings

Derived explicit rules for massive amplitude calculations.

Presented new master formulae for 4d massive theories.

Extended double copy structure to include massive particles.

Abstract

Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and gravity theories. This article extends this framework to worldsheet models for massive particles in 4d, obtained via a symmetry reduction of a higher dimensional massless model. The target space of the resulting models turns out to be the phase space of 4d massive particles in a twistorial representation, and so the worldsheet theory agrees with the two-twistor string previously introduced by the authors. However, the paper has been written so as to be largely self-contained. We discuss two interesting classes of massive theories in detail. For gauge theories, the reduction procedure is explicitly adapted to supersymmetric gauge theories on the Coulomb branch. For supergravity theories, the reduction is adapted to give theories obtained via Cremmer, Scherk and Schwartz (CSS) reduction, with broken supersymmetry and massive multiplets. The reduction procedure gives explicit and systematic rules to obtain amplitudes for all these theories and their amplitudes from two compact master formulae that have their origins in 6d based on the polarized scattering equations; in the CSS case the formulae are new, and in both cases their derivation is systematic. The freedom to include mass allows the definition of a loop insertion operator, thereby extending the formulae to 1-loop. Unlike the massless 4d twistorial models, these all display a perfect double copy structure, here incorporating massive particles in the relationship between gauge theory and CSS supergravity amplitudes.