Two-Loop Diagrammatics in a Self-Dual Background

TL;DR

This paper develops diagrammatic rules for two-loop QED diagrams in a self-dual background, revealing how the two-loop effective Lagrangian can be expressed in terms of one-loop diagrams, with implications for quantum field theory calculations.

Contribution

It introduces a diagrammatic approach for simplifying two-loop QED diagrams in a self-dual background, connecting two-loop and one-loop vacuum diagrams.

Findings

Two-loop effective Lagrangian expressed via one-loop diagrams.

Diagrammatic rules simplify complex two-loop calculations.

Connection parallels similar structures in SUSY Yang-Mills theory.

Abstract

Diagrammatic rules are developed for simplifying two-loop QED diagrams with propagators in a constant self-dual background field. This diagrammatic analysis, using dimensional regularization, is used to explain how the fully renormalized two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop diagrams. The connection between the two-loop and one-loop vacuum diagrams in a background field parallels a corresponding connection for free vacuum diagrams, without a background field, which can be derived by simple algebraic manipulations. It also mirrors similar behavior recently found for two-loop amplitudes in N=4 SUSY Yang-Mills theory.