Abstract
A closed-form expression is obtained for a holomorphic sector of the two-loop Euler–Heisenberg type effective action for N=2 supersymmetric QED derived in hep-th/0308136. In the framework of the background-field method, this sector is singled out by computing the effective action for a background N=2 vector multiplet satisfying a relaxed super self-duality condition. The approach advocated in this Letter can be applied, in particular, to the study of the N=4 super-Yang–Mills theory on its Coulomb branch.
Highlights
The Euler-Heisenberg Lagrangian corresponds to an approximation of slowly varying fields, and is a function of the field strength Fab only, LEH = L(F+2, F−2 )
There are no quantum corrections to Λ and Λbeyond second order in the field strength, Λ ∝ F+2, since no appropriate superfield invariant exists
The point is that the function Ω in (3) has the following general form
Summary
F+ and F− are the (anti) self-dual components of the field strength F , F± The point is that the function Ω in (3) has the following general form Ω(F+2), can be restored by computing the effective action for background vector supermultiplets satisfying a relaxed self-duality condition.
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