  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.
