Wilson line-based action for gluodynamics at the quantum level

TL;DR

This paper develops quantum corrections to a Wilson line-based action for gluodynamics, simplifying calculations of one-loop amplitudes by transforming the Yang-Mills action and systematically incorporating quantum effects.

Contribution

It introduces two methods to include quantum corrections in a Wilson line-based gluodynamics action, demonstrating their equivalence and efficiency for higher-multiplicity one-loop amplitude computations.

Findings

Both methods are equivalent in developing quantum corrections.

The Wilson line-based action simplifies tree-level amplitude calculations.

The first method is more efficient for higher-multiplicity one-loop amplitudes.

Abstract

We recently derived a new action for gluodynamics by canonically transforming the Yang-Mills action on light-cone. The transformation elimated triple gluons vertices and replaced the gauge fields with Wilson lines. This greatly reduced the number of diagrams required to compute tree level amplitudes. However, at the quantum level, the action turned out to be incomplete. We present two ways, based on one-loop effective action approach, to systematically develop quantum correction to our action. The first method retains Yang-Mills vertices in the loop, while the second method explicitly incorporates the interaction vertices of our action into the loop. We demonstrate that both approaches are equivalent, although the former appears to be more efficient for computing higher-multiplicity one-loop amplitudes.