Manifestly N=2N=2 supersymmetric regularization for N=2N=2 supersymmetric field theories

We formulate the higher covariant derivative regularization for N=2N=2 supersymmetric gauge theories in N=2N=2 harmonic superspace. This regularization is constructed by adding the N=2N=2 supersymmetric higher derivative term to the classical action and inserting the N=2N=2 supersymmetric Pauli–Villars determinants into the generating functional for removing one-loop divergencies. Unlike all other regularization schemes in N=2N=2 supersymmetric quantum field theory, this regularization preserves by construction the manifest N=2N=2 supersymmetry at all steps of calculating loop corrections to the effective action. Together with N=2N=2 supersymmetric background field method this regularization allows to calculate quantum corrections without breaking the manifest gauge symmetry and N=2N=2 supersymmetry. Thus, we justify the assumption about existence of a regularization preserving N=2N=2 supersymmetry, which is a key element of the N=2N=2 non-renormalization theorem. As a result, we give the proof of the N=2N=2 non-renormalization theorem which does not require any additional assumptions.