Self-duality, Helicity and Higher-loop Euler-Heisenberg Effective Actions

TL;DR

This paper explores the simplicity of the two-loop Euler-Heisenberg effective action in self-dual backgrounds, highlighting its connections to helicity, supersymmetry, and applications in quantum electrodynamics and supersymmetric theories.

Contribution

It reveals the natural expression of the two-loop Euler-Heisenberg Lagrangian in terms of one-loop quantities in self-dual backgrounds, linking to recent findings in supersymmetric gauge theories.

Findings

Simplified two-loop effective action in self-dual backgrounds

Connection between self-duality, helicity, and supersymmetry

Applications to helicity amplitudes and nonperturbative effects

Abstract

The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.