On the Yang-Mills two-loop effective action with wordline methods

TL;DR

This paper derives the two-loop effective action for pure Yang-Mills theory with constant field strength using worldline methods, confirming the correctness of the approach and reproducing known beta-function results.

Contribution

First derivation of the two-loop effective action in Yang-Mills theory using worldline formalism, demonstrating the method's consistency and accuracy.

Findings

Correctly reproduces the two-loop beta-function.

First application of worldline formalism to two-loop Yang-Mills effective action.

Validates the multiloop generalization procedure in the worldline approach.

Abstract

We derive the two-loop effective action for covariantly constant field strength of pure Yang-Mills theory in the presence of an infrared scale. The computation is done in the framework of the worldline formalism, based on a generalization procedure of constructing multiloop effective actions in terms of the bosonic worldline path integral. The two-loop beta-function is correctly reproduced. This is the first derivation in the worldline formulation, and serves as a nontrivial check on the consistency of the multiloop generalization procedure in the worldline formalism.