(α′)4 corrections to the N=2 supersymmetric Born–Infeld action

We consider the N=2 supersymmetric Born–Infeld action and compute one-loop divergences quantizing the theory in N=1 superspace. We find that in the presence of non constant curvature the theory is not renormalizable. The structure of the (α′)4 counterterm, proportional to derivatives of the curvature, is consistent with effective action calculations from superstring theory.