Wilson Lines and Boundary Operators of BCFW Shifts

TL;DR

This paper computes boundary operators for all BCFW shifts in Yang-Mills and QCD, revealing they can be organized into Wilson lines, linking boundary contributions to gauge-invariant non-local operators.

Contribution

It provides a comprehensive calculation of boundary operators for BCFW shifts, showing their organization into Wilson lines, a novel insight into gauge invariance and non-local operators in gauge theories.

Findings

Boundary operators correspond to boundary contributions in BCFW shifts.

Infinite series of boundary operators are organized into Wilson lines.

Results verified through explicit amplitude calculations.

Abstract

Boundary operators are gauge invariant operators whose form factors correspond to boundary contributions of BCFW shifts. In gauge theory, the boundary operators contain infinite series, which are constrained by gauge symmetry. We compute the boundary operators of all possible BCFW shifts in Yang-Mills theory and QCD, and show that the infinite series can be elegantly organized into Wilson lines, which are natural building blocks for non-local gauge invariant operators. We comment on their connection to jet functions and gauge invariant off-shell amplitudes. We also verify our results by studying various BCFW shifts of four and five-point amplitudes.