A Gluing Operator for the Ambitwistor String

TL;DR

This paper introduces a new gluing operator in the ambitwistor string framework that simplifies the recursive construction of scattering amplitudes and loop integrands, providing a unified approach to tree-level and one-loop calculations.

Contribution

It proposes a novel gluing operator that enables efficient computation of scattering amplitudes and loop integrands in ambitwistor string theory, connecting string propagators with field theory limits.

Findings

Derives the complete one-loop integrand in SYM and SUGRA.

Shows the gluing operator's role in recursive amplitude construction.

Conjectures the operator as the path integral form of the ambitwistor string propagator.

Abstract

We present a new operator in the ambitwistor string which glues together correlators with fewer points or of lower genus. It underpins the recursive construction of tree-level CHY scattering amplitudes by Dolan \& Goddard, as well as the computation of loop integrands on a Riemann sphere by Geyer et al. The gluing operator is a tractable object due to the finiteness of the spectrum. In particular, we demonstrate how it gives rise to the complete one-loop integrand in SYM and SUGRA. The operator is conjectured to be the path integral incarnation of the ambitwistor string propagator, and to coincide with the field theory limit of the standard string theory propagator.