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

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.