Wilson line-based action for gluodynamics at the loop level

TL;DR

This paper introduces quantum corrections to a Wilson line-based action for gluodynamics, enabling systematic inclusion of loop effects and validation through explicit amplitude calculations, thus enhancing the computational framework for high-energy QCD processes.

Contribution

It develops two equivalent methods to incorporate loop contributions into a vertex-eliminated Wilson line-based action, validated by explicit amplitude computations.

Findings

Validated the quantum completeness of the approach by computing 4-point one-loop amplitudes.

Demonstrated the equivalence of two methods for including loop effects.

Extended the framework to other Yang-Mills reformulations.

Abstract

We develop quantum corrections to the Wilson line-based action which we recently derived through a transformation that eliminates triple gluon vertices from the Yang-Mills action on the light-cone. The action efficiently computes high multiplicity tree-level split-helicity amplitudes with the number of diagrams following the Delannoy number series. However, the absence of the triple gluon vertices results in missing loop contributions. To remedy this, we develop two equivalent approaches using the one-loop effective action method to systematically incorporate loop contributions to our action. In one approach there are solely Yang-Mills vertices in the loop whereas the other uses the interaction vertices of our action along with the kernels of the solution of our transformation in the loop. In addition to demonstrating the equivalence of both approaches, we validated the quantum completeness of the former by computing all 4-point one-loop amplitudes which could not be previously computed. Both of our approaches are easily extendable to develop quantum corrections to other reformulations of the Yang-Mills theory obtained via non-linear classical field transformations eliminating interaction vertices.