Two-loop Yang-Mills theory in the world-line formalism and an Euler-Heisenberg type action

TL;DR

This paper develops a detailed two-loop Euler-Heisenberg type effective action for gluon loops in Yang-Mills theory using the world-line formalism, analyzing divergence structures and renormalization.

Contribution

It introduces a novel two-loop world-line formalism approach for Yang-Mills theory and explicitly computes divergence structures and renormalization procedures.

Findings

Exact two-loop moduli integrals performed with a mass parameter

Divergence coefficients identified for renormalization

Framework facilitates future calculations in gauge theories

Abstract

Within the framework of the world-line formalism we write down in detail a two-loop Euler-Heisenberg type action for gluon loops in Yang-Mills theory and discuss its divergence structure. We exactly perform all the world-line moduli integrals at two loops by inserting a mass parameter, and then extract divergent coefficients to be renormalized.