TWO-LOOP VACUUM DIAGRAMS IN BACKGROUND FIELD AND THE HEISENBERG–EULER EFFECTIVE ACTION

Abstract

We show that in arbitrary even dimensions, the two-loop scalar QED Heisenberg–Euler effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, when the constant background field satisfies F2 = -f2𝟙, which in four dimensions coincides with the condition for self-duality, or definite helicity. This result relies on new recursion relations between two-loop and one-loop diagrams, with background field propagators. It also yields an explicit form of the renormalized two-loop effective action in a general constant background field in two dimensions.