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

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.

23 pages, 2 figures; v2: minor changes, added references

References in corpus (15)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• Exacting N=4 Superconformal Symmetry
• Analytic form of the full two-loop five-gluon all-plus helicity amplitude
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• Dual Conformal Structure Beyond the Planar Limit
• Implications of nonplanar dual conformal symmetry
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• Conformal anomaly of generalized form factors and finite loop integrals
• Amplitudes from superconformal Ward identities
• Amplitudes from anomalous superconformal symmetry
• Augmented Recursion For One-loop Amplitudes

Cited by in corpus (10)

• On loop celestial amplitudes for gauge theory and gravity
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• The Full Color Two-Loop Six-Gluon All-Plus Helicity Amplitude
• An $n$-point QCD two-loop amplitude
• One-loop same helicity YM amplitudes from BG currents
• The dimension-shift conjecture for one-loop amplitudes
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
• Yangian Symmetry in Five Dimensions
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point