Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes

TL;DR

This paper demonstrates that one-loop all-plus helicity scattering amplitudes in Yang-Mills theory are conformally invariant and provides a formula making this symmetry manifest, advancing understanding of loop-level conformal properties.

Contribution

It introduces a new formula for one-loop all-plus amplitudes that explicitly exhibits conformal invariance and proves this using recursive techniques.

Findings

One-loop all-plus amplitudes are conformally invariant.

The paper provides a formula with manifest conformal symmetry.

Each term transforms covariantly under dual conformal variations.

Abstract

The massless QCD Lagrangian is conformally invariant and, as a consequence, so are the tree-level scattering amplitudes. However, the implications of this powerful symmetry at loop level are only beginning to be explored systematically. Even for finite loop amplitudes, the way conformal symmetry manifests itself may be subtle, e.g. in the form of anomalous conformal Ward identities. As they are finite and rational, the one-loop all-plus and single-minus amplitudes are a natural first step towards understanding the conformal properties of Yang-Mills theory at loop level. Remarkably, we find that the one-loop all-plus amplitudes are conformally invariant, whereas the single-minus are not. Moreover, we present a formula for the one-loop all-plus amplitudes where the symmetry is manifest term by term. Surprisingly, each term transforms covariantly under directional dual conformal variations. We prove the formula directly using recursive techniques, and check that it has the correct physical factorisations.