Two-Loop Diagrammatics in a Self-Dual Background

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.

16 pp, Latex, Axodraw

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• From effective actions to the background geometry
• "Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions
• On the Yang-Mills two-loop effective action with wordline methods
• A Gauge-Gravity Relation in the One-loop Effective Action