Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines

TL;DR

This paper establishes a connection between light-front perturbation theory and Wilson lines for off-shell gluon amplitudes, showing how recursion relations resum classes of graphs into gauge-invariant Wilson line matrix elements.

Contribution

It demonstrates that light-front recursion relations for off-shell amplitudes can be interpreted as Wilson lines, linking gauge invariance and diagram resummation in this formalism.

Findings

Recursion relations resum classes of graphs into Wilson lines.

Wilson lines provide a gauge-invariant framework for off-shell amplitudes.

Ward identities require additional instantaneous terms in light-front graphs.

Abstract

We analyze the off-shell scattering amplitudes in the framework of the light-front perturbation theory. It is shown that the previously derived recursion relation between tree level off-shell amplitudes in this formalism actually resums whole classes of graphs into a Wilson line. More precisely, we establish a correspondence between the light-front methods for the computation of the off-shell amplitudes and the approach which makes use of the matrix elements of straight infinite Wilson lines, which are manifestly gauge invariant objects. Furthermore, since it is needed to explicitly verify the gauge invariance of light-front amplitudes, it is demonstrated that the Ward identities in this framework need additional instantaneous terms in the light-front graphs.