A new Wilson line-based action for gluodynamics

TL;DR

This paper introduces a novel Wilson line-based classical action for gluodynamics that simplifies amplitude calculations by eliminating triple-gluon vertices, leading to fewer Feynman diagrams and matching known results.

Contribution

It presents a new canonical transformation of Yang-Mills fields resulting in an action with only MHV and related vertices, simplifying tree-level amplitude computations.

Findings

Agreement with standard amplitude calculations up to 8-point NNMHV

Fewer diagrams needed compared to CSW and standard Yang-Mills

Elimination of triple-gluon vertices simplifies the computational process

Abstract

We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $\overline{\textrm{MHV}}$ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any $n$-leg vertex has $2\leq m \leq n-2$ negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.