Towards exact results of QED from supersymmetry

To obtain some exact results of U(1) gauge theory (QED), we construct the low energy effective action of N=2 supersymmetric QED with a massless matter and Fayet-Iliopoulos term, assuming no confinement. The harmonic superspace formalism for N=2 extended supersymmetry makes the construction easy. We analyze the vacuum structure and find no vacuum. It suggests the confinement in non-supersymmetric QED at low energies.