A note on one-loop cluster adjacency in N $$ \mathcal{N} $$ = 4 SYM

Abstract

Abstract We study cluster adjacency conjectures for amplitudes in maximally supersymmetric Yang-Mills theory. We show that the n-point one-loop NMHV ratio function satisfies Steinmann cluster adjacency. We also show that the one-loop BDS-like normalized NMHV amplitude satisfies cluster adjacency between Yangian invariants and final symbol entries up to 9-points. We present conjectures for cluster adjacency properties of Plücker coordinates, quadratic cluster variables, and NMHV Yangian invariants that generalize the notion of weak separation.

Keywords

• Scattering Amplitudes
• Supersymmetric Gauge Theory
• Differential and Algebraic Geometry