Surface Kinematics and the Canonical Yang-Mills All-Loop Integrand

Journal Article · 27 April 2025 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.134.171601 · OSTI ID:2563435

Arkani-Hamed, Nima; Cao, Qu ; Dong, Jin ; Figueiredo, Carolina ; He, Song

It has been a long-standing challenge to define a canonical loop integrand for nonsupersymmetric gluon scattering amplitudes in the planar limit. Naive integrands are inflicted with $1/0$ ambiguities associated with tadpoles and massless external bubbles, which destroy integrand-level gauge invariance as well as consistent on-shell factorization on single loop cuts. In this Letter, we show that this essentially kinematical obstruction to defining “the” integrand for Yang-Mills theory has a structural solution, handed to us by the formulation of gluon amplitudes in terms of curves on surfaces. This defines “surface kinematics” generalizing momenta, making it possible to define the integrand satisfying both a (surface generalized) notion of gauge-invariance and consistent loop cuts. The integrand also vanishes at infinity in appropriate directions, allowing it to be recursively computed for nonsupersymmetric Yang-Mills theory in any number of dimensions. We illustrate these ideas through one loop for all multiplicity, and for the simplest two-loop integrand. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009988
• OSTI ID: 2563435
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 17 Vol. 134; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English