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

We formulate the higher covariant derivative regularization for N = 2 supersymmetric gauge theories in N = 2 harmonic superspace. This regularization is constructed by adding the N = 2 supersymmetric higher derivative term to the classical action and inserting the N = 2 supersymmetric Pauli-Villars determinants into the generating functional for removing one-loop divergencies. Unlike all other regularization schemes in N = 2 supersymmetric quantum field theory, this regularization preserves by construction the manifest N = 2 supersymmetry at all steps of calculating loop corrections to the effective action. Together with N = 2 supersymmetric background field method this regularization allows to calculate quantum corrections without breaking the manifest gauge symmetry and N = 2 supersymmetry. Thus, we justify the assumption about existence of a regularization preserving N = 2 supersymmetry, which is a key element of the N = 2 non-renormalization theorem. As a result, we give the proof of the N = 2 non-renormalization theorem which does not require any additional assumptions. (C) 2015 The Authors. Published by Elsevier B.V.